Answer:
y=2x+8 and y=-2x+7
Explanation:
The attached graphic shows the steps. Two distinctive features of a straight line in the form of y=mx+b are its slope, m, and its y-intercept, b. A quick look at the equations reveals that their slopes form unique pairs. The slopes in the first option are 2 and -2. The other slope pairs are b) 4 and -2, c) -3 and 3, and d) -2,-6. This means that if we calculate the slopes of lines p and r from the given points, there should only be one result that matches the combinations provided.
Set up a table for the points (see worksheet) and then pick any two points for each line to calculate slope. The slope is the Rise/Run of the line: the change in y for a change in x. The table uses the first and last points for each line, but any two points will work (for a straight line).
Lines p and r are found to have slopes of 2 and -2, respectively. That means their equations will take the form of:
p: y = 2x + b
r: y= -2x + b
We could (and will) work further to find the y-intercepts (b), but just looking at the answer options, it is clear that the first set of equations match the slope calculations exactly.
y = 2x+8, and y = -2x+7
None of the others come close. This is the answer. If this is a test, or you are missing a more interesting activity, stop here. But just to insure we are doing the work correctly, and that the ideas are understood, lets plot the two given equations and add the points, as shown on the worksheet. It is satisfying to find that the graph confirms our choice. The points all fall on the two lines. Another useful check is to find the y-intercepts (the value of y when x=0). Those are noted on the graph (0,7) for r, and (0,8) for p, and lend further confimration to our choice. Add these intercepts to the first equations that contain the y-intercept as b. b for line p is 8, b for line r is 7:
p: y = 2x + b
r: y= -2x + b
p: y = 2x + 8
r: y= -2x + 7
A perfect match to our selection. Calculating b is not needed based on the options presented, but a tougher question may require finding the y-intercept before making a choice.