a Since there are no ticks on the coordinate plane, we must choose which function matches which graph based on the steepness of each slope. We are given two functions.
&g(x)=6x+a, m=6
&h(x)=2x+b, m=2
Because the slope tells us how many units we move up for each unit we move to the right, a function with a slope of 6 will rise faster than a function with a slope of 2. Therefore, the functions can be assigned as shown.
b If we look at the slope-intercept form, y=mx+b, we can see that a in g(x) and b in h(x) are the y-intercepts of the functions.
Slope-Intercept Form: y&=mx+ b
Given function: g(x)&=6x+ a
Given function: h(x)&=2x+ b
c The first thing we are instructed to do is mark point C, which is on the line for function g and 2 units to the right of (p,q).
Now we can do the same thing for function h to mark point D.
We are asked to find the difference between the y-coordinates of points C and D. In the graphs above, we can see that point C was an increase of 12 with respect to the y-axis and point D was an increase of 4. We can find the difference by subtracting these quantities.
12-4=8
Therefore, the y-coordinate of C is 8 units greater than the y-coordinate of D.
