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2 years ago

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Write the equation of a line in slope intercept form that passes through the point ( -8, 2) and is parallel to the line y=1/4x−3

. y=1/4x+4 y−2=1/4(x+8) y=1/4x−6 y+8=1/4(x−2)

1 answer:

mel-nik [20]2 years ago

6 0

Y-2=1/4(x+8) is your answer
Explanation
Desmos

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Answer:

$\large\boxed{y=-\dfrac{1}{3}x-\dfrac{10}{3}\to x+3y=-10}$

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

<em>m</em><em> - slope</em>

<em>b</em><em> - y-intercept</em>

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (5, -5) and (-4, -2).

Substiute:

$m=\dfrac{-2-(-5)}{-4-5}=\dfrac{-2+5}{-9}=\dfrac{3}{-9}=-\dfrac{1}{3}$

Put the value of the slope and the coordinates of the point (5, -5) to the equation of a line:

$-5=-\dfrac{1}{3}(5)+b$

$-5=-\dfrac{5}{3}+b$ <em>add 5/3 to both sides</em>

$-\dfrac{15}{3}+\dfrac{5}{3}=b\\\\-\dfrac{10}{3}=b\to b=-\dfrac{10}{3}$

Finally we have the equation of a line in the slope-intercept form:

$y=-\dfrac{1}{3}x-\dfrac{10}{3}$

Convert to the standard form <em>(Ax + By = C)</em>:

$y=-\dfrac{1}{3}x-\dfrac{10}{3}$ <em>multiply both sides by 3</em>

$3y=-x-10$ <em>add x to both sides</em>

$x+3y=-10$

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