The equation of a line is [tex]y=\frac{-2}{3} x-\frac{5}{3}[/tex].
Solution:
Given slope, m = [tex]-\frac{2}{3}[/tex] and passes through the point (–3, –1).
Equation of a line passes through one point and slope formula:
[tex]y-y_1=m(x-x_1)[/tex]
Here, [tex]x_1=-3,y_1=-1[/tex] and [tex]m=-\frac{2}{3}[/tex]
Substitute these in the given formula, we get
⇒ [tex]y-(-1)=\frac{-2}{3} (x-(-1))[/tex]
⇒ [tex]y+1=\frac{-2}{3} (x+1)[/tex]
Cross multiply the fraction.
⇒ [tex]3(y+1)=-2 (x+1)[/tex]
⇒ [tex]3y+3=-2x-2[/tex]
Subtract 3 on both sides of the equation.
⇒ [tex]3y=-2x-2-3[/tex]
⇒ [tex]3y=-2x-5[/tex]
Divide by 3 on both sides of the equation.
⇒ [tex]y=\frac{-2}{3} x-\frac{5}{3}[/tex]
Hence, the equation of a line is [tex]y=\frac{-2}{3} x-\frac{5}{3}[/tex].
Answer:
D) y = -2/3x - 3
Step-by-step explanation:
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