Let <em>x</em> be the number of miles and <em>y</em> the total cost of the service.
Since the company <em>They Haul</em> charges $40 plus 0.20 per mile, then for <em>x</em> miles they would charge $40 plus 0.2x:
Since the company <em>Good Deal</em> charges $80 regardless of the number of miles, then:
To find the intersection of both equations, set both expressions to be equal and solve for <em>x:</em>
Then, the cost is the same for both companies if the amount of miles is equal to 200, and the cost would be $80.
To find the <em>y-intercept </em>for the company <em>They Haul</em>, evaluate the expression for <em>x=0:</em>
Since the expression for <em>Good Deal</em> does not depend on the value of <em>x</em>, then the <em>y-intercept </em>is:
To graph the equations:
Find two points on each line and draw a line through those points.
To find a point on a line, substitute different values of <em>x</em> to find the corresponding values of <em>y</em>.
For instance, choose <em>x=0 </em>and <em>x=100</em>. From the first equation, we obtain the following values for y:
Then, the points (0,40) and (100,60) belong to the first line. Plot those two points on a coordinate plane and then draw a line through those points:
For the other line, the value of <em>y</em> is always 80 regardless of the value of <em>x</em>. Then, the points (50,80) and (150,80) belong to the line. Do the same procedure to draw that second line:
We can see that <em>They Haul</em> (red) charges more than <em>Good Deal</em> whenever the number of miles is greater than 200.
The slope-intercept form of the equation of a line with slope <em>m</em> and y-intercept <em>b </em>is:
We already knew the equations for <em>They Haul</em> and <em>Good Deal</em>:
They Haul:
The slope is equal to 0.2
Good Deal:
Since the x-variable does not appear, than means that the coefficient of <em>x</em> is 0, so the slope is equal to 0.