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3.03 Review: Equations of lines


There are many different ways to write the equation of a line, depending on the information we've been given in the problem. Here is a quick review:

Writing the equation of a line
  1. Slope-intercept form: $y=mx+b$y=mx+b  where $m$m is the slope and $b$b is the y-intercept. (To be used when we have the slope and can easily find the y-intercept)
  2. Point-slope form: $y-y_1=m(x-x_1)$yy1=m(xx1)   where $(x_1,y_1)$(x1,y1) is a point on the line.  (Best used when we have one point and the slope, or two points and can easily compute the slope.)
  3. Horizontal line:$y=c$y=c where $c$c is any constant. Horizontal lines have a slope equal to zero.
  4. Vertical line: $x=c$x=c where $c$c is any constant. Vertical lines have an undefined slope.

Use the questions below and the question set to practice writing equations given different sets of information.


Practice questions


Write down the equation of a line whose slope is $-8$8 and crosses the $y$y-axis at $-9$9. Express in slope-intercept form.


Line L1 has the following equation: $y=x-2$y=x2

  1. Find the $y$y value of the $y$y-intercept of the line.

  2. Find the $x$x value of the $x$x-intercept of the line.

  3. Find the $y$y-coordinate of a point that has an $x$x-coordinate of $-5$5.

  4. Plot the line $y=x-2$y=x2 on the number plane.

    Loading Graph...


After finding the equation, we could also rewrite it in Standard Form.

Standard form of the equation of a line

 $Ax+By=C$Ax+By=C where $A$A, $B$B, and $C$C must be integers and the value of $A$A is positive.


Practice questions


A line has slope $-\frac{3}{2}$32 and passes through the point ($2$2, $-2$2).

  1. By substituting into the equation $y=mx+b$y=mx+b, find the value of $b$b for this line.

  2. Hence write the equation of the line in slope-intercept form.

  3. Derive the same equation by using the point-slope formula.

  4. Graph the line.

    Loading Graph...


A line passes through the points ($3$3, $-5$5) and ($-7$7, $2$2).

  1. Find the slope of the line.

  2. Find the equation of the line by substituting the slope and one point into $y-y_1=m\left(x-x_1\right)$yy1=m(xx1).

    You may express the equation in slope intercept or standard form.

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