Parallel and perpendicular lines

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.

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.

The graph of the line x + y = 3 is shown on this grid.

By drawing a suitable line on the grid, solve these simultaneous equations.

x + y = 3 and y = 2 x - 3

Umi says,

The simultaneous equations y = 2x + 3 and 2y – 4x = 7 will have no solutions.

Is Umi correct? Explain how you decide.

The diagram shows a circle with centre (0, 0) and a tangent at (12, 5^-). The tangent at (12, 5^-) crosses the x-axis at (p, 0).

Find the exact value of p. You must show your working.

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 diagram shows a circle, centre the origin, with the tangent to the circle at the point (4, 2).

Write down the equation of the circle.

Show that the tangent to the circle at the point (4, 2) has gradient - 2.

Find the equation of the tangent to the circle at the point (4, 2).

Write down an equation for the line that is parallel to y = 3 x - 5 and passes through the point (0, 1).

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.

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

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.

The graph below shows a circle with centre (0, 0) and equation x² + y² = 169.

Show that the point (- 12, 5) lies on the circumference of the circle.

Find the equation of the tangent to the circle at the point (- 12, 5), giving your answer in the form y = mx + c.

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.

Here is a sketch of the circle x² + y² = 45.

Find the equation of the tangent at the point (-3, 6).

Line AB is shown on this coordinate grid.

Write down the coordinates of

point A,

point B.

Plot point C on the grid at (7, – 2).

The equation of line AB is y = 2 x + 1. A line parallel to AB goes through the point (0, 4).

Write down the equation of the parallel line.

The diagram shows a circle with centre (0, 0) and a tangent at the point (– 12, 16).

The tangent crosses the y-axis at the point (0, p).

Find the value of p.

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.

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.

The point (- 5, 2) lies on the circumference of a circle, centre (0, 0).

Find the equation of the circle.

Work out the gradient of the tangent to the circle at (- 5, 2).

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.

A straight line passes through the point (0, 6) and is perpendicular to y = 4 x - 5.

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

Work out the coordinates of the intersection of the graphs of y = 4x - 5 and y = x² - 17.

The diagram shows a circle, centre the origin.

Write down the equation of the circle.

Point P has coordinates (8, –6).

Show that point P lies on the circle.

Find the equation of the tangent to the circle at point P.

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.