Equation of a Line Practice

Find the equation of the line which has gradient 2 and crosses the y-axis at y = 5.

Find the equation of the line which has gradient -3 and crosses the y-axis at y = 20.

Find the equation of the line which has gradient 2 and passes through the point (1, 8).

Find the equation of the line that passes through the points (1, 4) and (5, 16).

The line y = 5x – 13 passes through the point R. The point R has y co-ordinate 2. Find the x co-ordinate of point R.

The line y = 10 – 3x passes through the point T. The point T has x co-ordinate 4. Find the y co-ordinate of point T.

The line y = 2x + 11 passes through the points U and V. The point U has y co-ordinate 19. The point V has x co-ordinate -3. (a) Find the x co-ordinate of point U. (b) Find the y co-ordinate of point V.

Does the line y = 3x + 11 pass through the point (3, 20)?

Does the line y = 4x – 7 pass through the point (2, 1)?

The line Q passes through the points (-2, 20) and (3, 5). (a) Find the equation of Q. (b) Does Q pass through the point (-5, 29)?

Answer explanation

First find the value of slope, m=-3

so our main equation becomes y=3x+c

To find intercept c

Substitute any of the points (either (-2,20) or (3,5) ) in the above equation: y=-3x+c , then we will get the value of c= 14

so the equation of the line becomes y=-3x+14

Now in order to check whether the point (-5,29) is on the line, substitute the value of x as -5 in the equation

y=-3*-5 +14

= 15 +14

=29

Since the y- coordinate is 29, we can say that the point (-5,29) will be on the line