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3.03 Review: Equations of lines

Lesson

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

QUESTION 1

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.

QUESTION 2

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

QUESTION 3

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...

QUESTION 4

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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