Question

find the equation of the graphed line.
a. $y = -2x + 5$
b. $y = -\frac{2}{5}x + 2$
c. $y = 2x + 5$
d. $y = -\frac{5}{2}x + 5$

Explanation:

Step1: Identify y-intercept

The line crosses the y-axis at (0, 5), so \( b = 5 \) (slope-intercept form \( y = mx + b \)).

Step2: Calculate slope (m)

Use two points, e.g., (0, 5) and (2, 1). Slope \( m=\frac{1 - 5}{2 - 0}=\frac{-4}{2}=-2 \).

Step3: Form equation

Substitute \( m = -2 \) and \( b = 5 \) into \( y = mx + b \), get \( y=-2x + 5 \).

Answer:

a. \( y = -2x + 5 \)