Question

a line has a slope of $-2$ and passes through the point $(3,5)$. which of the following is the equation of the line?
a. $y = -2x + 11$
b. $y = -2x + 3$
c. $y = -2x + 5$
d. $y = -2x - 1$

Explanation:

Step1: Recall point-slope form

The point-slope formula is \( y - y_1 = m(x - x_1) \), where \( m=-2 \), \( x_1=3 \), \( y_1=5 \).

Step2: Substitute values into formula

\( y - 5 = -2(x - 3) \)

Step3: Simplify to slope-intercept form

\( y - 5 = -2x + 6 \), then \( y = -2x + 11 \)

Answer:

a. \( y = -2x + 11 \)