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Math  /  Algebra

QuestionWhich equation describes the same line as y−5=−2(x+4)y-5=-2(x+4) ? A. y=−2x−3y=-2 x-3 B. y=−2x−2y=-2 x-2 C. y=−2x+9y=-2 x+9 D. y=−2x−8y=-2 x-8

Studdy Solution

STEP 1

1. We are given the equation of a line in point-slope form: y−5=−2(x+4) y - 5 = -2(x + 4) .
2. We need to convert this equation to slope-intercept form to compare it with the given options.
3. The slope-intercept form of a line is y=mx+b y = mx + b , where m m is the slope and b b is the y-intercept.

STEP 2

1. Convert the given equation from point-slope form to slope-intercept form.
2. Simplify the equation to find the y-intercept.
3. Compare the simplified equation with the given options to find the correct one.

STEP 3

Start with the given equation: y−5=−2(x+4) y - 5 = -2(x + 4)

STEP 4

Distribute the −2-2 on the right-hand side: y−5=−2x−8 y - 5 = -2x - 8

STEP 5

Add 55 to both sides to isolate yy: y=−2x−8+5 y = -2x - 8 + 5

STEP 6

Simplify the equation: y=−2x−3 y = -2x - 3

STEP 7

Compare the simplified equation y=−2x−3 y = -2x - 3 with the given options.
The equation that describes the same line is:
y=−2x−3 \boxed{y = -2x - 3}

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