Gradient and intercept

PQ is perpendicular to QR.

Work out the value of a.

A circle has centre (2, 3) and radius 5 A straight line passes through (3, 7) and has a gradient of 2

Work out the coordinates of the two points where the circle and the straight line intersect.

The equation of a straight line is 2 ax + y = 25 where a is a constant. The line passes through the point (3, 1)

Work out the value of the gradient of the line.

C is a point on the straight line AB.

AC: CB = 3: 2

Work out the equation of the straight line passing through O and C.

The equations of two straight lines are

y – 3 x = 4 and 6 y = 18 x – 5

Show that the lines are parallel.

S (7, 2) and T (5, – 4) are points on a straight line.

Work out the gradient of the line.

Work out the distance between S and T. Give your answer in the form a where a and b are both integers greater than 1

A line passes through P (1, k) and Q (r, 6) where k and r are constants. The midpoint of PQ has x-coordinate 5 The gradient of the line is 2

Work out the value of k.

Line K has equation 4 x – 5 y = 17 Line L passes through the points (3, 6) and (– 5, 16)

Tick (✓) the correct statement about lines K and L.

Show working to support your answer.

The point (–6, –4) lies on a straight line with gradient

Work out the coordinates of the point where the line crosses the y-axis.

Line A has equation y + 4 x = 6 Line B is parallel to line A and passes through the point (2, 1) The point (d, 2 d) lies on line B.

Work out the value of d.

Here are four sketch graphs.

Circle the letter of the sketch graph that represents 3 x + 2 y = 5

A and B are points on the line y = 3 x + 2 B, C and D (5, 0) are points on the line L. O A: AC = 1: 4

Work out the x-coordinate of B.