3 years ago

Write the equation of a line in slope-intercept form that goes through the points (-4, 3) and (-5, 1). Show your work.

Mathematics

1 answer:

Neporo4naja [7]3 years ago

7 0

M=1-3/-5-4
M=-2/-9
M=2/9

y=2/9x+c
let y=3 and x=-4
3=2/9<span>(-4)+c
3=-8/9+c
3+8/9=c
C=35/9

y=2/9x+35/9
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$\large\boxed{y=-\dfrac{2}{3}x+\dfrac{13}{3}}$

Step-by-step explanation:

$\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\===============================$

$\text{We have the point:}\\\\(5,\ 1)\ \text{and}\ (-4,\ 7).\ \text{Substitute:}\\\\m=\dfrac{7-1}{-4-5}=\dfrac{6}{-9}=-\dfrac{6:3}{9:3}=-\dfrac{2}{3}\\\\\text{We have the equation in form:}\\\\y=-\dfrac{2}{3}x+b\\\\\text{Put the coordinates of the point (5, 1) to the equation:}\\\\1=-\dfrac{2}{3}(5)+b\\\\1=-\dfrac{10}{3}+b\qquad\text{add}\ \dfrac{10}{3}\ \text{to the both sides}\\\\\dfrac{3}{3}+\dfrac{10}{3}=b\to b=\dfrac{13}{3}\\\\\text{Finally:}\\\\y=-\dfrac{2}{3}x+\dfrac{13}{3}$