Straight line graphs

Here are lines A and B.

Complete these statements.

Write down the equation of a straight line parallel to y – 2 x = 9

A straight line

• has gradient 5

• passes through the point (3, 7)

Circle the equation of the line.

y = 3 x – 2 y = 3 x + 7 y = 5 x y = 5 x – 8

Write down the equation of a straight line parallel to y – 2 x = 9

A straight line

• has gradient 5

• passes through the point (3, 7)

Circle the equation of the line.

y = 3 x – 2 y = 3 x + 7 y = 5 x y = 5 x – 8

On the grid, identify the region represented by

Label the region R.

A circle has centre (0, 0) and circumference 36 π

Work out the equation of the circle.

Point J has coordinates (15, 0) and point K has coordinates (30, – 5)

Work out the equation of the straight line through J and K.

Straight line LM has equation y = 4 x – 7 Straight line ST has equation y =

Are the lines LM and ST perpendicular? Tick a box.

Give a reason for your answer.

A triangle is drawn using the lines y = x x = – 2

Work out the coordinates of the three vertices of the triangle.

A triangle is drawn using the lines y = x x = – 2

Work out the coordinates of the three vertices of the triangle.

Here is a table of values for the equation y = 3 x + 1

Draw the graph of y = 3 x + 1 for values of x from 1 to 4

Work out the value of y when x = 2.5

y =

A straight line passes through points A (– 5, 9), B and C (3, – 7).

AB: BC = 1: 3

Work out the coordinates of point B.

Work out the equation of the line perpendicular to AC that passes through C.

On the grid, draw the graph of y = 2 x – 6 for values of x from – 2 to 5

Write down the equation of a line parallel to y 3x 1

Line A is perpendicular to line B. The gradient of line A is – 2

Work out the gradient of line B.

A straight line passes through (3, 14) and (12, 32)

Work out the equation of the line. Give your answer in the form y = mx + c

A straight line passes through (3, 14) and (12, 32)

Work out the equation of the line. Give your answer in the form y = mx + c

Points P, Q and R (8, 22) form a triangle.

PQ is a horizontal line, with P on the y-axis. Angle PRQ is a right angle. The gradient of PR is 2 Work out the coordinates of Q.

Craig wants to draw a graph, for values of x from – 3 to 3, where the x-coordinate and y-coordinate are always in the ratio 2: 1 Here is his graph.

Make two criticisms of Craig’s graph.

The x-values in the table make a linear sequence. The y-values in the table make a different linear sequence.

Complete the table.

Draw a straight line passing through the points (0, 3), (2, 7) and (4, 11)

Use the graph to work out the value of y when x = 3

Lines AB and BC are shown.

Write down the coordinates of C.

Write down the coordinates of the midpoint of AB.

D is the point on the grid that makes ABCD a parallelogram. Work out the coordinates of D.

Write down the equation of the line passing through A and B.

A straight line is perpendicular to the straight line through (2, 8) and (6, 15) and passes through (0, 9) and (x, 17) Work out the value of x.

x =

Juice and water are mixed together in the ratio 2: 7

Draw a straight line graph that shows the amounts of juice and water to mix together. Your graph must show up to 10 litres of juice.

How much water needs to be mixed with 5 litres of juice?

A straight line has gradient 6 and passes through the point (3, 19) Work out the equation of the line. Give your answer in the form y = mx + c

A straight line has gradient 6 and passes through the point (3, 19) Work out the equation of the line. Give your answer in the form y = mx + c

A straight line passes through O and (2, 6)

Circle the equation of the line.

Circle the equation of the line parallel to y = 5 x + 2

y = 2 x + 5 y = 5 x – 2 y = – 5 x + 2 y = – 2 x – 5

Circle the equation of the line that is parallel to y = + 3

Line A has equation y = 4 x – 1 Line B is perpendicular to line A and passes through the point (8, 5) Work out the coordinates of the point where line B intersects the x-axis.

Draw the graph of y = 3 x – 1 for values of x from – 1 to 3

(– 3, 10) is a point on line L. (4, 0) and (6, 10) are points on line M. L and M are parallel.

Work out the equation of line L. Give your answer in the form y = mx + c

The graph below is used to convert between temperature in degrees Fahrenheit (F) and temperature in degrees Celsius (C).

Use the graph to convert 40 degrees Fahrenheit into degrees Celsius.

At one temperature, T, the number of degrees Celsius is double the number of degrees Fahrenheit. The graph of C = 2 F can be drawn to help find this temperature.

On the grid opposite, draw the graph of C = 2 F for values of F from –25 to 25 You may use the table to help you.

Use your graph to estimate the value of T. Give your answer in degrees Celsius.

Here is line L and the graph of y = x – 1 The scales of the axes are not shown.

Work out the equation of line L.

A straight line has gradient 4 and passes through the point (5, 23)

Work out the equation of the line. Give your answer in the form y = mx + c

A straight line has gradient 4 and passes through the point (5, 23) Work out the equation of the line. Give your answer in the form y = mx + c

Lee wants to draw the graph of y = x for values of x from –5 to 5 Here is his graph.

Make two different criticisms of his graph.

The graph of y = 4 – x for values of x from –2 to 5 is shown on the grid.

On the grid, draw the graph of y = 2 x – 5 for values of x from –2 to 5

Use your graph to solve 2 x – 5 = 4 – x

x =

Show that the lines y = 3 x + 7 and 2 y – 6 x = 8 are parallel. Do not use a graphical method.

Is the point (–5, –6) above, below or on the line y = 3 x + 7 ? Tick one box.

You must show your working. Do not use a graphical method.

Show that the lines y = 3 x + 7 and 2 y – 6 x = 8 are parallel. Do not use a graphical method.

Is the point (–5, –6) above, below or on the line y = 3 x + 7 ? Tick one box.

You must show your working. Do not use a graphical method.

Draw the graph of y = 0.8 for values of x from 0 to 6

Two straight lines intersect at point A.

Circle the coordinates of A.

The equation of a straight line is 3 x + 2 y = 24 Circle the point where the line crosses the x-axis.

(0, 8) (12, 0) (0, 12) (8, 0)

On the grid, draw the graph of x + y = 2 for values of x from –3 to 3

Circle the equation of the line that is parallel to the x-axis.

y = –5 x – y = 0 x = 3 x + y = 0

P and Q are points on the line 3 x + 2 y = 6

Complete the coordinates of P and Q.

Draw the line 3 x + 2 y = 6 for values of x from –3 to 3

A is the point (2, –5) B is the point (4, –9)

Show that the gradient of the straight line passing through A and B is –2

C is the point (–301, 601)

Does C lie on the straight line passing through A and B ? You must show your working.