Gradient and intercept

A straight line, L, is parallel to the line with equation y = 2 – 5 x The line L passes through the point (0, 6)

Find an equation of the line L

On the grid below, draw the graph of y x 1 for values of x from 2 to 3

On the grid, draw the graph of y = 2 x – 3 for values of x from –2 to 4

Line L is drawn on the grid.

Find an equation for L Give your answer in the form y = mx + c

Line L is drawn on the grid.

Find an equation for L Give your answer in the form y = mx + c

On the grid, draw the graph of y = 5 − 2 x for values of x from –2 to 3

A straight line passes through the points with coordinates (0, –3) and (2, 0)

Find an equation of the line.

A straight line passes through the points with coordinates (0, –3) and (2, 0)

Find an equation of the line.

A is the point with coordinates (–5, 12)

B is the point with coordinates (19, –48)

Find an equation of the straight line that passes through the points A and B

The diagram shows three points, A, B and C, and a line EF on a grid.

Write down the coordinates of the point A

The coordinates of the point D are (3, –2)

On the grid, mark with a cross () the position of D Label the cross D

Find the coordinates of the midpoint of BC

Write down the equation of the line EF

Write down the value of (m + 2)⁰ where m is a positive integer.

Simplify (3a²b⁴)³

Factorise fully 14x²y⁴ + 21x³y²

The diagram shows a straight line drawn on a grid.

Write down an equation of the line.

Write down the value of (m + 2)⁰ where m is a positive integer.

Simplify (3a²b⁴)³

Factorise fully 14x²y⁴ + 21x³y²

The diagram shows a straight line drawn on a grid.

Write down an equation of the line.

ABCD is a trapezium with AB parallel to DC

A is the point with coordinates (–4, 6) B is the point with coordinates (2, 3) D is the point with coordinates (–1, 8)

The trapezium has one line of symmetry. The line of symmetry intersects CD at the point E

Work out the coordinates of the point E

Line L is drawn on the grid.

Find an equation for L Give your answer in the form y = mx + c

Here are nine graphs.

Complete the table below with the letter of the graph that could represent each given equation. Write each answer on the dotted line.

Equation	Graph
y = –2x + 3	.......................................................
y = – 1x	.......................................................
y = tanx	.......................................................
y = (x + 1)(x – 1)(x – 2)	.......................................................

The straight line L has equation 2 y + 7 x = 10

Find the gradient of L

Find the coordinates of the point where L crosses the y‑axis.

The straight line L has equation 2 y + 7 x = 10

Find the gradient of L

Find the coordinates of the point where L crosses the y‑axis.

Write down an equation of the straight line with gradient –3 and which passes through the point with coordinates (0, 5)

Show, by shading on the grid, the region defined by all three of the inequalities

Label the region R

Write down an equation of the straight line with gradient –3 and which passes through the point with coordinates (0, 5)

Show, by shading on the grid, the region defined by all three of the inequalities

Label the region R

ABC is a triangle in which angle ABC = 90°

p and q are integers such that

the coordinates of A are (p, 10) the coordinates of B are (–1, –5) the coordinates of C are (8, q)

Given that the gradient of AC is –

work out the value of p and the value of q

Point A has coordinates (5, 8) Point B has coordinates (9, –4)

Work out the gradient of AB.

The straight line L has equation y = –4x + 5

Write down the gradient of a straight line that is perpendicular to L.

ABC is an isosceles triangle with AB = AC.

B is the point with coordinates (–1, 5) C is the point with coordinates (2, 10) M is the midpoint of BC.

Find an equation of the line through the points A and M. Give your answer in the form py + qx = r where p, q and r are integers.

On the grid, draw the graph of y = 3x – 2 for values of x from –1 to 4

On the grid, draw the graph of y = 7 – 4x for values of x from −2 to 3

Find the gradient of the straight line with equation 5 x + 2 y = 7

The line L is shown on the grid.

Find an equation for L.

The point A has coordinates (5, −4) The point B has coordinates (13, 1)

Work out the coordinates of the midpoint of AB.

Line L has equation y= 2 − 3x

Write down the gradient of line L.

Line L has equation y= 2 − 3x

Does the point with coordinates (100, −302) lie on line L? You must give a reason for your answer.

The point A has coordinates (5, −4) The point B has coordinates (13, 1)

Work out the coordinates of the midpoint of AB.

Line L has equation y= 2 − 3x

Write down the gradient of line L.

Line L has equation y= 2 − 3x

Does the point with coordinates (100, −302) lie on line L? You must give a reason for your answer.

Use the graph to find an estimate for the gradient of the curve at P.

Hence find an equation of the tangent to the curve at P. Give your answer in the form y=mx+c

The equation f (x) =k has exactly two different solutions for −4≤ x ≤12

Use the graph to find the two possible values of k.

H is the point with coordinates (−4, 1) J is the point with coordinates (j, 15) where j <0 K is the point with coordinates (6, k)

M is the midpoint of JK. The gradient of HM is 2

Find the value of j and the value of k.

The straight line L has gradient 5 and passes through the point with coordinates (0, í3)

Write down an equation for L.

The region R, shown shaded in the diagram, is bounded by four straight lines.

Write down the inequalities that define R.

Line L is drawn on the grid.

Find an equation for L.

On the grid, draw the graph of y = 2 x + 3 for values of x from í2 to 3

Show, by shading on the grid, the region that satisfies all three of the inequalities

Label the region R.

The diagram shows a quadrilateral ABCD on a centimetre grid.

Work out the area of triangle ABC. You must include the units with your answer.

Give a reason why angle ACD is equal to angle CAB.

Write down an equation for the straight line that passes through D and C.

On the grid, draw the graph of y = 2 x + 3 for values of x from í2 to 4