Question

question 1 pts. which equation represents the graphed line? a ( y - 1 = -2(x - 3) ) b ( y - 1 = -2(x + 3) ) c ( y + 1 = -2(x - 3) ) d ( y + 1 = -2(x + 3) )

Explanation:

Step1: Identify two points on the line

From the graph, the line passes through (3,1) and (0,7).

Step2: Calculate the slope

Slope \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 1}{0 - 3} = \frac{6}{-3} = -2 \)

Step3: Use point-slope form

Point-slope form: \( y - y_1 = m(x - x_1) \). Using (3,1) and \( m=-2 \): \( y - 1 = -2(x - 3) \)

Step4: Verify the equation

Check if (0,7) satisfies it: \( 7 - 1 = -2(0 - 3) \Rightarrow 6 = 6 \), which is true. So the equation is correct.

Answer:

A. \( y - 1 = -2(x - 3) \)