Straight line graphs

For each of the algebraic statements below decide whether it is an equation or an identity.

(x - 1)(x - 2) = 12 is an........

A straight line is parallel to y = 3 x and passes through the point (2, 11).

Find the equation of the line in the form y = mx + c.

A straight line has equation y = 5 x + 2.

Write down the gradient of the line.

Find the value of y when x = 7.

Make x the subject of y = 5 x + 2.

For each of the algebraic statements below decide whether it is an equation or an identity.

(x - 1)(x - 2) = 12 is an........

A straight line is parallel to y = 3 x and passes through the point (2, 11).

Find the equation of the line in the form y = mx + c.

Sketch the graph of y = 4 on the axes below. Show clearly the value of any intercepts.

A straight line has equation y = 4 x + 9.

Write down the gradient of the line.

Casey says the graph of y = 4 x + 9 passes through the point (3, 23).

Is Casey correct? Show how you decide.

In the diagram below, the shaded region is a parallelogram. The parallelogram can be identified by four inequalities. Two of the inequalities are y ⩾ 6 and y ⩾ x.

Write down the other two inequalities that identify the parallelogram.

Work out the area of the parallelogram. You must show your working.

(b)........ square units

This grid shows a vertical line going through the point P.

Write down the coordinates of point P.

Plot the point (4, - 1).

Write down the equation of the vertical line going through point P.

Below are six graphs, numbered 1 to 6, that show different relationships between x and y.

Graph 1
Graph 2
Graph 3

Graph 4
Graph 5
Graph 6

y y y

For each description below, write down the number of the graph that best represents the relationship between x and y.

x: temperature in °C y: temperature in °F, where y = 1.8 x + 32. Graph........

x: average speed when running 200 m y: time taken to run 200 m. Graph........

x: mass of a solid object made from clay y: volume of the same solid object. Graph........

The region R is shown on this grid.

The region R is defined by three inequalities. The first inequality is given below.

Complete the second inequality and write down the third inequality needed to define region R.

y ⩾ 0

2 y........ 3 x + 6

A straight line passes through the points (0, 5) and (2, 13).

Find the equation of the line in the form y = mx + c.

Part of the graph of y = 2 x + 1 is drawn on this grid.

Write down the y-intercept.

The line continues to the right.

Will the line pass above, below or through the point (40, 80)? Show how you decide.

The line y = 2 x + 1 will pass........ the point (40, 80) because........

Write down the equation of a line that is parallel to y = 2 x + 1.

The graph of y = x is drawn on the grid.

The region R satisfies the following inequalities.

y ⩾ x y ⩽ 2 y < - 2 x - 3

By drawing two more straight lines on the grid, find and label the region R.

Hiro and Taylor are both electricians. Hiro does not charge to visit a house but charges a fixed rate per hour for the work needed.

This graph shows the relationship between the hours worked and the total charge made by Hiro.

Explain how this graph shows that Hiro’s total charge is directly proportional to the hours worked.

Taylor does charge to visit a house and charges the same fixed rate per hour as Hiro for the work needed.

On the axes above, draw a graph to show the relationship between the hours worked and

the total charge made by Taylor.

The graphs of x = - 3 and y = - x are drawn on the grid.

The region R satisfies the following inequalities.

By drawing one more line, find and label the region R.

A rhombus is drawn on a coordinate grid. One diagonal of the rhombus has equation y = + 3. The other diagonal passes through the point (1, 7).

Find the equation of the other diagonal of the rhombus. Give your answer in the form y = mx + c.

Sketch the graph of y = - 2. Show clearly the value of any intercepts.

Sketch the graph of y = x - 3. Show clearly the value of any intercepts.

Sketch the graph of y = x².

A ball of dough is left to rise before it is baked. The graph shows the height of the ball of dough over the first 20 minutes.

Work out the gradient of the line as a decimal, giving the units of your answer. Show how you work out your answer.

A baker works out the height of the ball of dough at the end of 25 minutes as 14 cm.

Use your gradient to show that the baker could be correct.

What assumption has the baker made?

Find the equation of the line through (4, 5) that is perpendicular to y = 2 x - 3.

The region R is shown on this grid. A is the point (0, 3) and B is the point (3, 4.5).

Show that an equation of the straight line through A and B is 2 y = x + 6.

Write down the three inequalities that define region R.

The graph shows a parallelogram ABCD.

A has coordinates (0, - 6), B has coordinates (3, 0) and C has coordinates (9, 0).

Find the equation of the line that passes through the points C and D, giving your answer in the form y = mx + c. You must show your working.

For each graph below, select its possible equation from this list.

A y = x³ B y = -2 C y = -x

D x = -2 E y = x² F y = 2x + 1

Write the letter of the equation beneath each graph.

A straight line has the equation y = 2 x - 1.

Write down the gradient of the line.

Here are the equations of four straight lines.

Which of the four straight lines is parallel to y = 2 x - 1 ?

A student says

y = x + 4 is the steepest of the four straight lines because it has the largest number added.

Explain why the student is wrong.

Here is part of the graph of y = 2 x - 1.

The line continues to the right.

Will the line pass above, below or through the point (45, 90)? Show how you decide.

The line y = 2 x - 1 will pass........ the point (45, 90) because........

A straight line passes through the point (8, 1) and is perpendicular to the line y = 4 x - 2.

Find the equation of the line, giving your answer in the form y = mx + c.

This graph shows part of a straight line.

Write down the y-intercept.

Show that the gradient of the line is -2.

Write down the equation of the line.

The line continues to the right.

Will this line pass through the point (50, -103)? Show how you decide.

This graph shows part of a straight line.

Show that the gradient of the line is 2.5.

Write down the equation of the line.

The graphs of y = x and y = - 2 are drawn on the grid.

The region R satisfies the following inequalities.

y ⩾ - 2 y ⩽ x y < 4 - 2 x

By drawing one more line, find and label the region R.

Complete the table for y = x² - 4x + 1.

Draw the graph of y = x² - 4x + 1 for -1 ⩽ x ⩽ 5.

On the same grid, draw the graph of y = 2 x - 6 for - 1 ⩽ x ⩽ 5.

Use your graphs to solve the equation x² - 4x + 1 = 2x - 6.

Give your answers to 1 decimal place.

Complete this table for y = 4 x - 2.

On the grid below, draw the graph of y = 4 x - 2 for values of x from 0 to 4.

The diagram below shows part of another straight line.

Find the equation of this straight line.

The graph shows two parallel lines, Line A and Line B.

Line A has equation y = 6 x + 7. Line B passes through the point (4, 26).

Find the equation of Line B.

Region R satisfies these inequalities.

y > 3 y ⩾ x x + y ⩽ 9

By drawing three straight lines on the grid, find and label the region R.

The graph shows two parallel lines, Line A and Line B.

Line A has equation y = 6 x + 7. Line B passes through the point (4, 26).

Find the equation of Line B.

Write down the equation of each of these lines.

Sketch the graph of y = x².

This graph shows part of a straight line.

Write down the y-intercept.

This graph shows part of another straight line.

Find the gradient of this line.

This line is continued to the right.

Will the line pass through the point (200, 102)? Show how you decide.

P is the point (0, - 1) and Q is the point (5, 9).

Find the equation of the line through P that is perpendicular to the line PQ.

The diagram shows the lines y = 2 x + 1 and 7 x + 4 y = 28.

The region R satisfies these inequalities.

y ⩽ 2 x + 1 7 x + 4 y ⩾ 28
y > 1

By drawing a third straight line, find and label the region R that satisfies these inequalities.

This grid shows a horizontal line going through the point A.

Write down the coordinates of point A.

(a)(i) (........,........)

Plot the point (- 2, 3).

Write down the equation of the horizontal line going through point A.

The diagram shows a straight line that passes through points A and B, and a curve that passes through points P and Q.

Find the equation of the straight line.

The equation of the curve is y = x² + kx + 8.

Find the value of k.

Diann draws line BQ. She says

Triangle ABQ is isosceles.

Is Diann correct? You must show all your working.

A company tests a new battery for an electric car. The distance the car travels, d km, and the charge left in the battery, C %, are measured.

Some measurements are shown in the table.

Plot these values on the grid and use them to draw a straight line.

Use your line to estimate the greatest distance the car will travel.

What assumption is made when estimating the greatest distance?

For your line in part (a), find

the gradient,

the C-axis intercept.

Use your answers to part (c) to write down the equation of your graph.

Give your equation in the form C = ad + b.

Use your equation to find the value of C when d = 210.

Comment on your answer.

Find the coordinates of the point where y – 2 x = 1 crosses the y-axis.

The diagram shows the graph of y = 3 x + c, where c is a constant.

Find the value of k.

The diagram below shows a 1 cm coordinate grid.

Find an inequality that defines region A and another inequality that defines region B.

Shade the region on the grid given by the inequality y ⩾ 6.

A fourth shaded region, given by the inequality

y ⩾ kx + 2,

is added to the grid.

The unshaded region now has area 23 cm².

Find the value of k.

Point A has coordinates (- 4, 6) and point B has coordinates (8, 3).

Find the gradient of line AB.

Find the equation of line AB.

Point P has coordinates (0, - 2).

Write down the equation of the line parallel to line AB that passes through P.