Question

Write in​ point-slope form an equation of the line through the pair of points. (3,12) and (5,9)

Answer 1

Answer:

$\large\boxed{y=-\dfrac{3}{2}x+16\dfrac{1}{2}\to y=-1.5x+16.5}$

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (3, 12) and (5, 9).

Substitute:

$m=\dfrac{9-12}{5-3}=\dfrac{-3}{2}=-\dfrac{3}{2}$

Put the value of a slope and coordinates of the point (3, 12) to the equation of a line:

$12=-\dfrac{3}{2}(3)+b$

$12=-\dfrac{9}{2}+b$

$12=-4\dfrac{1}{2}+b$          add $4\dfrac{1}{2}$ to both sides

$16\dfrac{1}{2}=b\to b=16\dfrac{1}{2}$

Finally:

$y=-\dfrac{3}{2}x+16\dfrac{1}{2}$