Question

which equation matches the graph?
y= 2x + 3
y= 2/3x +2
y = -2/3x + 2
y=-2x + 3

Explanation:

Step1: Analyze the slope sign

The graph is decreasing, so the slope (m) should be negative. Eliminate options with positive slopes: \( y = 2x + 3 \) (slope \( 2>0 \)) and \( y=\frac{2}{3}x + 2 \) (slope \( \frac{2}{3}>0 \)).

Step2: Find the y - intercept

The graph crosses the y - axis at \( (0, 2) \), so the y - intercept \( b = 2 \).

Step3: Determine the slope

We can use two points on the line. Let's take \( (0, 2) \) and \( (3, 0) \). The slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 2}{3 - 0}=-\frac{2}{3} \). So the equation is \( y =-\frac{2}{3}x + 2 \).

Answer:

\( y =-\frac{2}{3}x + 2 \) (the blue - colored option: \( y = - 2/3x+2 \))