Question

6.01] Select the system of equations that corresponds to the given graph.

graph of two lines. One line goes through the points 0 comma negative 4 and 4 comma 0. The other line goes through the points 1 comma 2 and 4 comma 0
Select one:
a. 4x + 2y = 12
4x + 2y = 4
b. 2x + 3y = 4
6x + 9y = 12
c. 2x + 4y = 12
2x + y = 3
d. 2x + 3y = 8
−x + y = −4

Answer 1

Okay, so, if one line goes through (0,-4) and (4,0), first we find the slope with these two points. Slope=y2-y1/x2-x1. We can plug our points in: 0-(-4)/4-0=4/4=1. That is the slope of our first line. We plug that into our slope-intercept form equation, as well as one of the points (either one, doesn't matter):

y=1x+b --> -4=1(0)+b --> -4=b

So, if we plug all of our new information in, our first line is: y=x-4.

Your answers are all in standard form, so put our new equation into standard form:

y-x=x-x-4
y-x=-4 or -x+y=-4

If you want, I could go through finding the second line, but we can already see that the answer is d :)