MATH SOLVE

10 months ago

Q:
# Which equation represents the line that passes through the points (3-,7) and (3,3)? A) y = 2/3 x + 1B) y = -2/3 x + 9C) y = 2/3 x + 9D) y = - 2/3 x + 5

Accepted Solution

A:

The slope-intercept form:[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, 7) and (3, 3). Substitute:[tex]m=\dfrac{3-7}{3-(-3)}=\dfrac{-4}{6}=-\dfrac{2}{3}[/tex][tex]y=-\dfrac{2}{3}x+b[/tex]Put the coordinates of the point (3, 3) to the equation of a line:[tex]3=-\dfrac{2}{3}(3)+b[/tex][tex]3=-2+b[/tex] add 2 to both sides[tex]5=b\to b=5[/tex]Answer: [tex]\boxed{y=-\dfrac{2}{3}x+5}\to\boxed{D)}[/tex]