Question

19 the graph of a line is shown on the grid. the coordinates of both points indicated on the graph of the line are integers. what is the rate of change of y with respect to x for this line? a 5/2 b -6/5 c 2/3 d -5/6

Explanation:

Step1: Select two points on the line

Let's take two integer - valued points. Suppose the points are \((x_1,y_1)\) and \((x_2,y_2)\). From the graph, we can take \((x_1,y_1)=(0, 5)\) and \((x_2,y_2)=(6,0)\).

Step2: Use the slope formula

The rate of change of \(y\) with respect to \(x\) (slope \(m\)) is given by the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substitute \(x_1 = 0,y_1=5,x_2 = 6,y_2 = 0\) into the formula: \(m=\frac{0 - 5}{6-0}=-\frac{5}{6}\).

Answer:

D. \(-\frac{5}{6}\)