Question

Write an equation in a slope-intercept form for the line described.

Answer 1

$\bf (\stackrel{x_2}{-4}~,~\stackrel{y_2}{6})\qquad \qquad \qquad slope = m\implies -2 \\\\\\ \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-6=-2[x-(-4)] \\\\\\ y-6=-2(x+4)\implies y-6=-2x-8\implies y=-2x-2\\\\ -------------------------------\\\\ (\stackrel{x_2}{2}~,~\stackrel{y_2}{5})\qquad \qquad \qquad slope = m\implies 1 \\\\\\ \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-5=1(x-2) \\\\\\ y-5=x-2\implies y=x+3$

Answer 2

The slope-intercept form: y = mx + b

1. m = -2 → y = -2x + b

(-4, 6) → x = -4, y = 6, substitute:

6 = -2(-4) + b

6 = 8 + b |-8

b = -2

Answer: y = -2x - 2

2. m = 1 → y = 1x + b

(2, 5) → x = 2, y = 5, substitute:

5 = 1(2) + b |-2

b = 3

Answer: y = x + 3