Question

1. find the slope of the line containing (-3, 4) and (5, -2).
2. find the equation of the line containing (-2, -3) with m = -\frac{3}{4}

Explanation:

Step1: Recall slope formula

The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$

Step2: Substitute $(-3,4)$ and $(5,-2)$

$m=\frac{-2 - 4}{5 - (-3)}=\frac{-6}{8}$

Step3: Simplify the fraction

$m=-\frac{3}{4}$

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Step1: Recall point-slope form

Point-slope form: $y - y_1 = m(x - x_1)$

Step2: Substitute $(-2,-3)$ and $m=-\frac{3}{4}$

$y - (-3)=-\frac{3}{4}(x - (-2))$

Step3: Simplify to slope-intercept form

$y + 3=-\frac{3}{4}(x + 2)$
$y + 3=-\frac{3}{4}x - \frac{3}{2}$
$y=-\frac{3}{4}x - \frac{3}{2} - 3$
$y=-\frac{3}{4}x - \frac{9}{2}$

Answer:

1. $-\frac{3}{4}$
2. $y=-\frac{3}{4}x - \frac{9}{2}$ (or in standard form: $3x + 4y = -18$)