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Math  /  Algebra

Question2. What is an equation of the line that has slope -4 and passes through the point (−2,−5)(-2,-5) ? m=−4m=-4 F. y=−4x−8y=-4 x-8 G) y=−4x−13y=-4 x-13 H. y=−4x−5y=-4 x-5 x. y=−4x+3y=-4 x+3
3. What is an equation of the line that passes through the points (−4,3)(-4,3) and (−1,6)(-1,6) ? ג. y=−x−7y=-x-7
8. y=−x−1y=-x-1 e. y=7x+1y=7 x+1 D. y=x+7y=x+7

Studdy Solution

STEP 1

1. We are given the slope of the line and a point through which the line passes for the first problem.
2. We are given two points through which the line passes for the second problem.
3. We need to find the equation of the line in the form y=mx+b y = mx + b .

STEP 2

1. For the first problem, use the point-slope form to find the equation of the line.
2. For the second problem, calculate the slope of the line using the two given points, then use the point-slope form to find the equation of the line.

STEP 3

For the first problem, use the point-slope form of the equation of a line, which is y−y1=m(x−x1) y - y_1 = m(x - x_1) , where m m is the slope and (x1,y1) (x_1, y_1) is the point on the line.
Given: m=−4 m = -4 Point: (−2,−5) (-2, -5)
Substitute the given values into the point-slope form:
y−(−5)=−4(x−(−2)) y - (-5) = -4(x - (-2))
Simplify the equation:
y+5=−4(x+2) y + 5 = -4(x + 2)

STEP 4

Distribute the slope on the right side:
y+5=−4x−8 y + 5 = -4x - 8
Subtract 5 from both sides to solve for y y :
y=−4x−8−5 y = -4x - 8 - 5
y=−4x−13 y = -4x - 13
The equation of the line is y=−4x−13 y = -4x - 13 .
This corresponds to option G.

STEP 5

For the second problem, calculate the slope m m using the formula m=y2−y1x2−x1 m = \frac{y_2 - y_1}{x_2 - x_1} .
Given points: (−4,3) (-4, 3) and (−1,6) (-1, 6)
Substitute the coordinates into the slope formula:
m=6−3−1−(−4) m = \frac{6 - 3}{-1 - (-4)}
m=33 m = \frac{3}{3}
m=1 m = 1

STEP 6

Use the point-slope form of the equation of a line with the calculated slope and one of the points, say (−4,3) (-4, 3) .
y−3=1(x−(−4)) y - 3 = 1(x - (-4))
Simplify the equation:
y−3=x+4 y - 3 = x + 4
Add 3 to both sides to solve for y y :
y=x+4+3 y = x + 4 + 3
y=x+7 y = x + 7
The equation of the line is y=x+7 y = x + 7 .
This corresponds to option D.

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