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Write an equation for the line that passes through the points (-4,3) and -8,5)​

User Ken K
by
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1 Answer

7 votes

Answer:


y=\displaystyle- (1)/(2) x+1

Explanation:

Hi there!

Linear equations are typically organized in slope-intercept form:
y=mx+b where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis).

1) Determine the slope (m)


m=\displaystyle(y_2-y_1)/(x_2-x_1) where two points that fall on the line are
(x_1,y_1) and
(x_2,y_2)

Plug in the given points (-4,3) and (-8,5)​:


m=\displaystyle(3-5)/(-4-(-8))\\\\m=\displaystyle(-2)/(-4+8)\\\\m=\displaystyle(-2)/(4)\\\\m=\displaystyle- (1)/(2)

Therefore, the slope of the line is
\displaystyle- (1)/(2). Plug this into
y=mx+b:


y=\displaystyle- (1)/(2) x+b

2) Determine the y-intercept (b)


y=\displaystyle- (1)/(2) x+b

Plug in one of the points and solve for b:


3=\displaystyle- (1)/(2) (-4)+b\\\\3=2+b\\b=1

Therefore, the y-intercept is 1. Plug this back into the equation:


y=\displaystyle- (1)/(2) x+1

I hope this helps!

User Norman Gray
by
8.5k points

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