Ontario 10 Applied (MFM2P)
topic badge
Find equation of a line

We have now looked at a number of ways of finding the equation of a straight line. 

Equation of Lines!

We have:

$y=mx+b$y=mx+b  (slope-intercept form)

$ay+bx-c=0$ay+bxc=0   (general form)

$y-y_1=m\left(x-x_1\right)$yy1=m(xx1)   (point-slope formula)

$\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$yy1xx1=y2y1x2x1 (two point formula)

It's now time to practice using these different forms.

Worked Examples


A line has the equation $3x-y-4=0$3xy4=0.

  1. Express the equation of the line in slope-intercept form.

  2. What is the slope of the line?

  3. What is the $y$y-value of the $y$y-intercept of the line?


A straight line passes through the point ($0$0, $\frac{3}{4}$34) with slope $2$2.

  1. Find the equation of the line in the form $y=mx+b$y=mx+b.

  2. Express this equation in the general form $ax+by+c=0$ax+by+c=0.

  3. Find the $x$x-intercept.


Consider the line with equation: $3x+y+2=0$3x+y+2=0

  1. Solve for the $x$x-value of the $x$x-intercept of the line.

  2. Solve for the $y$y-value of the $y$y-intercept of the line.

  3. Plot the line.

    Loading Graph...


Answer the following.

  1. Find the equation, in general form, of the line that passes through $A$A$\left(-12,-2\right)$(12,2) and $B$B$\left(-10,-7\right)$(10,7).

  2. Find the $x$x-coordinate of the point of intersection of the line that goes through $A$A and $B$B, and the line $y=x-2$y=x2.

  3. Hence find the $y$y-coordinate of the point of intersection.




Determine the equation of a line, given its graph, the slope and y-intercept, the slope and a point on the line, or two points on the line.

What is Mathspace

About Mathspace