Question

15 the graph of a linear function is shown on the grid. which equation is best represented by this graph? a y = -\frac{7}{4}x + 4 b y = -\frac{7}{4}x + 7 c y = -\frac{4}{7}x + 4 d y = -\frac{4}{7}x + 7

Explanation:

Step1: Identify y - intercept

The line crosses the y - axis at the point (0, 7), so the y - intercept \(b = 7\).

Step2: Calculate the slope

Pick two points on the line, say (0, 7) and (7, 3). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{3 - 7}{7-0}=\frac{- 4}{7}\).

Step3: Use slope - intercept form

The slope - intercept form of a line is \(y=mx + b\). Substituting \(m =-\frac{4}{7}\) and \(b = 7\) gives \(y=-\frac{4}{7}x + 7\).

Answer:

D. \(y =-\frac{4}{7}x + 7\)