Question

Which equation is graphed here?

A) y = 2 +
2
3
x
B) y = -2 -
2
3
x
C) y =
2
3
x - 2
Eliminate
D) y = -
2
3
x + 2

Answer 1

The equation that is graphed there you can determine simply using any two points there:
1) For example, let's use points of the intersection with xy-plane: they are (0, 2) and (3, 0).
2) Then, find the slope using the formula
`m = (y_(2) - y_(1))/(x_(2) - x_(1))` where (x1, y1) is the first point, and (x2, y2) is the second one.
What is slope? Slope is the measure of how y changes when x changes. Find it using the formula and points (0. 2), (3, 0):
m = (0 - 2) / (3 - 0) = -2/3
3) Now, use the following point-slope formula:

`y - y_(0) = m(x - x_(0))`
where m is the slope, y and x are variables (do not touch them), and (x0, y0) is absolutely any point on the graph. Use, for example, point (3, 0) there. Plug in:
y - 0 = (-2/3)(x - 3)
y = -2x/3 + 2
SO, the answer will be y = -2x/3 + 2, or the option D.
Hope this helps!