Answer:
y = -x + 9
Step-by-step explanation:
You are given (-5,14), (-2,11), (1,8), and (4,5). Your first objective is to find the slope.
Slope is delta y divided by delta x - the amount of height the graph gains divided by the amount of horizontal length the graph gains. Take any two points and plug it into this: [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex].
i.e. (-2,11) and (4,5): [tex]\frac{11-5}{-2-4}[/tex] which is [tex]\frac{6}{-6}[/tex], or -1. Thus, the slope is -1.
We now have y = -1(x) + b, or just y = -x + b.
Next, find the y-intercept. Set the value of x to 0, as the y-intercept is found along the y-axis, which is at the horizontal center of the graph, 0. We now know that the y-intercept is (0,y). To find the y-value, plug one of the coordinate pairs of choice into x and y.
i.e. (-5,14): 14 = (-1)(-5) + b
14 = 5 + b
14 - 5 = 5 + b - 5
9 = b
So, the y-intercept is (0,9).
Finally, the equation is:
y = -x + 9
