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?
\\(\circ\\) a. $y = -2x - 1$
\\(\circ\\) b. $y = -2x + 11$
\\(\circ\\) c. $y = -2x + 5$
\\(\circ\\) d. $y = -2x + 3$

Explanation:

Step1: Recall point-slope form

Point-slope form: $y - y_1 = m(x - x_1)$ where $m=-2$, $(x_1,y_1)=(3,5)$

Step2: Substitute values into formula

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

Step3: Simplify to slope-intercept form

$y - 5 = -2x + 6$ → $y = -2x + 11$

Answer:

b. $y = -2x + 11$