Question

1. write the equation of the line between the following two points in point - slope form.

a. (3, -5) and (1, 2)
b. (-4, 2) and (8, 5)

Explanation:

Step1: Calculate slope for (3,-5) & (1,2)

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{2-(-5)}{1-3}=\frac{7}{-2}=-\frac{7}{2}$

Step2: Write point-slope form (use (3,-5))

Point-slope formula: $y-y_1=m(x-x_1)$
$y-(-5)=-\frac{7}{2}(x-3)$ or $y+5=-\frac{7}{2}(x-3)$

Step3: Calculate slope for (-4,2) & (8,5)

$m=\frac{5-2}{8-(-4)}=\frac{3}{12}=\frac{1}{4}$

Step4: Write point-slope form (use (-4,2))

$y-2=\frac{1}{4}(x-(-4))$ or $y-2=\frac{1}{4}(x+4)$

Answer:

a. $y+5=-\frac{7}{2}(x-3)$ (or using the other point: $y-2=-\frac{7}{2}(x-1)$)
b. $y-2=\frac{1}{4}(x+4)$ (or using the other point: $y-5=\frac{1}{4}(x-8)$)