Question

16. Which equation best represents the relationship between x and y in the graph? y 9 8 7 6 6 5 3 2 х -9-8-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 -2 4 5 -9 5 3 A. y = -x+3 y B. y = --x + 5 3 C. V=Y - 7

Answer 1

To determine which equation fits the relationship in the graph is best to determine the slope and y-intercept of the line.

The y-intercept is the point where the line crosses the y-axis. If you look at the graph said the point is (0,-3)

To determine the slope of the line you need to use two points, for example (4, 0) and (7, 2), and the formula:

$m=\frac{y_1-y_2}{x_1-x_2}$

Where

(x₁,y₁) are the coordinates of one of the points

(x₂,y₂) are the coordinates of the second point

$m=\frac{2-0}{7-4}=\frac{2}{3}\cong0.666\cong0.7$

The line that best represents the line is the last one (option D.)

$y=\frac{5}{7}x-3$

Because its slope is

$m=\frac{5}{7}=0.71\ldots$

And its y-intercept is (0,-3)