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QuestionFind the equation of the line through (−1,−4)(-1,-4) parallel to 3x+y=53x+y=5. Choices: y=3x+1y=3x+1, y=−3x+7y=-3x+7, y=−3x−7y=-3x-7, y=3x−1y=3x-1.

Studdy Solution

STEP 1

Assumptions1. We are given a point through which the line passes, (−1,−4)(-1,-4). . We are given a line 3x+y=53x + y =5 to which the required line is parallel.
3. We know that parallel lines have the same slope.
4. We are asked to find the equation of the line.

STEP 2

First, we need to find the slope of the given line. We can do this by rewriting the equation of the line in slope-intercept form, y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.
x+y=5x + y =5

STEP 3

Subtract 3x3x from both sides of the equation to isolate yy.
y=−3x+5y = -3x +5

STEP 4

Now, we can see that the slope of the given line is −3-3.

STEP 5

Since parallel lines have the same slope, the slope of the line we are trying to find is also −3-3.

STEP 6

Now we can use the point-slope form of a line, y−y1=m(x−x1)y - y1 = m(x - x1), where (x1,y1)(x1, y1) is a point on the line and mm is the slope.

STEP 7

Plug in the given point (−1,−4)(-1,-4) and the slope −3-3 into the point-slope form of the line.
y−(−4)=−3(x−(−1))y - (-4) = -3(x - (-1))

STEP 8

implify the equation.
y+4=−3(x+1)y +4 = -3(x +1)

STEP 9

istribute the −3-3 on the right side of the equation.
y+4=−3x−3y +4 = -3x -3

STEP 10

Subtract 44 from both sides of the equation to isolate yy.
y=−3x−3−4y = -3x -3 -4

STEP 11

implify the equation to get the final form.
y=−3x−7y = -3x -7So, the equation of the line through (−,−4)(-,-4) and parallel to the line 3x+y=53x + y =5 is y=−3x−7y = -3x -7.

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