Straight line graphs

The straight line L is shown on the grid.

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

In the diagram A is the point (0, 8) B is the point (16, 0) The point D divides the line segment AB in the ratio 1: 3 The line L passes thr h D.

L passes through the point with coordinates (–2,f) Show that f –4

C is a circle with centre (0, 0) The straight line with equation 3 x – 2 y = 52 is the tangent to C at the point P. Find the coordinates of P.

On the grid, reflect the shaded shape in the mirror line.

Write down the equation of the mirror line.

The point P has coordinates (–4, 5) The point Q has coordinates (6, –6) The point R has coordinates (k, k + 3) Given that angle PRQ is a right angle, find the possible values of k. You must show all your working.

Line L is drawn on the grid.

Find an equation for line L.

OBCD is a rectangle. DCE is a straight line.

B has coordinates (2, −4) E has coordinates (12, −6.5) Work out the coordinates of D. You must show all your working.

Here is a straight line L drawn on a grid.

Find an equation for L.

M is a different straight line with equation y = 5x

Write down the equation of a straight line parallel to M.

Here is a straight line L drawn on a grid.

Find an equation for L.

M is a different straight line with equation y = 5x

Write down the equation of a straight line parallel to M.

C is a circle with centre (0, 0) L is a straight line. The circle C and the line L intersect at the points P and Q. The coordinates of P are (5, 10) The x coordinate of Q is –2 L has a positive gradient and crosses the y-axis at the point (0, k) Find the value of k.

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

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

The straight line L has equation 2 y = 3 x – 7 Find an equation of the straight line perpendicular to L that passes through (6, –5)

The line L is shown on the grid.

Find an equation for L.

The line L is shown on the grid.

Find an equation for L.

Write down the coordinates of point B.

Plot the point with coordinates (4, –2) Label this point C.

Write down the coordinates of the midpoint of AB.

Draw the line with equation y = – 4

15The equation of line L₁ is y = 2x – 5 The equation of line L₂ is 6y + kx – 12 = 0 L₁ is perpendicular to L₂ Find the value of k. You must show all your working.

Here are the equations of two straight lines.

Oscar says that these lines are parallel. Is Oscar correct? You must give a reason for your answer.

The shaded region shown on the grid is bounded by four straight lines.

Find the four inequalities that define the shaded region.

Write down the coordinates of point A.

On the grid, mark with a cross () the point (1, 4) Label this point B.

On the grid, draw the line with equation y = ‒3

The centre of a circle is the point with coordinates (−1, 3) The point A with coordinates (6, 8) lies on the circle. Find an equation of the tangent to the circle at A. Give your answer in the form ax + by + c = 0 where a, b and c are integers.

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

12The equation of the line L₁ is y = 2x + 3 The equation of the line L₂ is 5y − 10x + 4 = 0 Show that these two lines are parallel.

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

20The diagram shows the graph of x² + y² = 30.25

Use the graph to find estimates for the solutions of the simultaneous equations x² + y² = 30.25 y – 2x = 1

Here is a sketch of the line L.

The points P(–6, 0) and Q(0, 3) are points on the line L. The point R is such that PQR is a straight line and PQ:QR = 2: 3

Find the coordinates of R.

Find an equation of the line that is perpendicular to L and passes through Q.

15The straight line L₁ has equation y = 3x – 4 The straight line L₂ is perpendicular to L₁ and passes through the point (9, 5) Find an equation of line L₂

C is a circle with centre the origin. A tangent to C passes through the points (–20, 0) and (0, 10) Work out an equation of C. You must show all your working.

The straight line L has equation 3 x + 2 y = 17

The point A has coordinates (0, 2) The straight line M is perpendicular to L and passes through A.

Line L crosses the y-axis at the point B. Lines L and M intersect at the point C.

Work out the area of triangle ABC. You must show all your working.

Complete the table of values for y = 4 x – 6

On the grid, draw the graph of y = 4x – 6 for values of x

Here is the graph of y = x² – 3

Use the graph to find estimates for the solutions to the equation x² – 2x – 2 = 0 You must show how you get your solutions.

On the grid below, draw the graph of y = 2x – 3 for values of x IURP í WR

On the grid below, draw the graph of y = 2x – 3 for values of x IURP í WR

The straight line L has the equation 3 y = 4 x + 7 The point A KDV FRRUGLQDWHV í Find an equation of the straight line that is perpendicular to L and passes through A.

Write down the coordinates of point A.

On the grid, draw the line with equation x = −4

The straight line L₁ passes through the points with coordinates (4, 6) and (12, 2) The straight line L₂ passes through the origin and has gradient −3

The lines L₁ and L₂ intersect at point P.

Find the coordinates of P.

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

The point P has coordinates (3, 4) The point Q has coordinates (a, b)

A line perpendicular to PQ is given by the equation 3 x + 2 y = 7

Find an expression for b in terms of a.

The line L is shown on the grid.

Find an equation for L.

The line L is shown on the grid.

Find an equation for L.

Write down the coordinates of the point A.

Plot the point with coordinates (2, 9). Label this point B.

Does point B lie on the straight line with equation y = 4 x + 1? You must show how you get your answer.

On the grid, draw the line with equation x = –2

ABCD is a rectangle.

A, E and B are points on the straight line L with equation x + 2 y = 12 A and D are points on the straight line M.

AE = EB

Find an equation for M.

A triangle has vertices PQ and R.

The coordinates of P are (−3, −6) The coordinates of Q are (1, 4) The coordinates of R are (5, −2)

M is the midpoint of PQ. N is the midpoint of QR.

Prove that MN is parallel to PR. You must show each stage of your working.

The equation of the line L₁ is y = 3x – 2 The equation of the line L₂ is 3y – 9x + 5 = 0

Show that these two lines are parallel.

Write down the three inequalities that define the shaded region.