Question

100 POINTS+BRAINLIEST 8TH GRADE MATH PT 5: WRITE THE EQUATION OF A LINE- this one was strange because the slope is supposed to be a negative fraction but that never appeared in the answer choices so please explain why I got it wrong thanks!!

Answer 1

Answer:

$\textsf{b.} \quad 3x+5y=2$

Step-by-step explanation:

Define the given points:

$\textsf{let}\:(x_1,y_1)=(4,-2)$

$\textsf{let}\:(x_2,y_2)=(-1,1)$

Use the slope formula to determine the slope of the line:

$\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-(-2)}{-1-4}=\dfrac{1+2}{-1-4}=-\dfrac{3}{5}$

Use the point-slope formula to determine the equation of the line.

$\implies y-y_1=m(x-x_1)$

Substitute the found slope and point (4, -2):

$\implies y-(-2)=-\dfrac{3}{5}(x-4)$

$\implies y+2=-\dfrac{3}{5}(x-4)$

Multiply both sides by 5:

$\implies 5(y+2)=-3(x-4)$

Expand the brackets:

$\implies 5y+10=-3x+12$

Add 3x to both sides:

$\implies 5y+10+3x=-3x+12+3x$

$\implies 3x+5y+10=12$

Subtract 10 from both sides:

$\implies 3x+5y+10-10=12-10$

$\implies 3x+5y=2$

Answer 2

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