Write in point-slope form an equation of the line through the pair of points. (3,12) and (5,9)
Accepted Solution
A:
Answer:[tex]\large\boxed{y=-\dfrac{3}{2}x+16\dfrac{1}{2}\to y=-1.5x+16.5}[/tex]Step-by-step explanation:The slope-intercept form of an equation of a line:[tex]y=mx+b[/tex]m - slopeb - y-interceptThe formula of a slope:[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]We have the points (3, 12) and (5, 9).Substitute:[tex]m=\dfrac{9-12}{5-3}=\dfrac{-3}{2}=-\dfrac{3}{2}[/tex]Put the value of a slope and coordinates of the point (3, 12) to the equation of a line:[tex]12=-\dfrac{3}{2}(3)+b[/tex][tex]12=-\dfrac{9}{2}+b[/tex][tex]12=-4\dfrac{1}{2}+b[/tex] add [tex]4\dfrac{1}{2}[/tex] to both sides[tex]16\dfrac{1}{2}=b\to b=16\dfrac{1}{2}[/tex]Finally:[tex]y=-\dfrac{3}{2}x+16\dfrac{1}{2}[/tex]