QuestionFind the line parallel to $y=-3x+7$ that passes through the point $(1,3)$ .

Studdy Solution

STEP 1

Assumptions1. The equation of the line we want to find is parallel to $y=-3x+7$ . The line passes through the point $(1,3)$ 3. The slope of a line parallel to another line is the same as the slope of the original line

STEP 2

First, we need to find the slope of the given line. The slope of a line in the form $y=mx+b$ is $m$ .
The given line is $y=-x+7$ , so the slope is $-$ .

STEP 3

Since the line we want to find is parallel to the given line, its slope is also $-3$ .

STEP 4

The equation of a line in slope-intercept form is $y=mx+b$ , where $m$ is the slope and $b$ is the y-intercept. We know the slope of our line is $-3$ , so the equation of our line is $y=-3x+b$ .

STEP 5

To find the y-intercept $b$ , we can use the point $(1,3)$ that the line passes through. Substituting $x=1$ and $y=3$ into the equation gives us $3=-3(1)+b$ .

STEP 6

olving for $b$ gives us $b=3+3=6$ .

STEP 7

Substituting $b=6$ into the equation of our line gives us the final equation $y=-3x+6$ .
So, the equation of the line parallel to $y=-3x+7$ that goes through the point $(1,3)$ is $y=-3x+6$ .

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QuestionFind the line parallel to $y=-3x+7$ that passes through the point $(1,3)$ .

Studdy Solution

STEP 1

Assumptions1. The equation of the line we want to find is parallel to $y=-3x+7$ . The line passes through the point $(1,3)$ 3. The slope of a line parallel to another line is the same as the slope of the original line

STEP 2

First, we need to find the slope of the given line. The slope of a line in the form $y=mx+b$ is $m$ .
The given line is $y=-x+7$ , so the slope is $-$ .

STEP 3

Since the line we want to find is parallel to the given line, its slope is also $-3$ .

STEP 4

The equation of a line in slope-intercept form is $y=mx+b$ , where $m$ is the slope and $b$ is the y-intercept. We know the slope of our line is $-3$ , so the equation of our line is $y=-3x+b$ .

STEP 5

To find the y-intercept $b$ , we can use the point $(1,3)$ that the line passes through. Substituting $x=1$ and $y=3$ into the equation gives us $3=-3(1)+b$ .

STEP 6

olving for $b$ gives us $b=3+3=6$ .

STEP 7

Substituting $b=6$ into the equation of our line gives us the final equation $y=-3x+6$ .
So, the equation of the line parallel to $y=-3x+7$ that goes through the point $(1,3)$ is $y=-3x+6$ .

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QuestionFind the line parallel to y=−3x+7y=-3x+7y=−3x+7 that passes through the point (1,3)(1,3)(1,3).

Studdy Solution

STEP 1

Assumptions1. The equation of the line we want to find is parallel to y=−3x+7y=-3x+7y=−3x+7 . The line passes through the point (1,3)(1,3)(1,3)3. The slope of a line parallel to another line is the same as the slope of the original line

STEP 2

First, we need to find the slope of the given line. The slope of a line in the form y=mx+by=mx+by=mx+b is mmm.The given line is y=−x+7y=-x+7y=−x+7, so the slope is −-−.

STEP 3

Since the line we want to find is parallel to the given line, its slope is also −3-3−3.

STEP 4

The equation of a line in slope-intercept form is y=mx+by=mx+by=mx+b, where mmm is the slope and bbb is the y-intercept. We know the slope of our line is −3-3−3, so the equation of our line is y=−3x+by=-3x+by=−3x+b.

STEP 5

To find the y-intercept bbb, we can use the point (1,3)(1,3)(1,3) that the line passes through. Substituting x=1x=1x=1 and y=3y=3y=3 into the equation gives us 3=−3(1)+b3=-3(1)+b3=−3(1)+b.

STEP 6

olving for bbb gives us b=3+3=6b=3+3=6b=3+3=6.

STEP 7

Substituting b=6b=6b=6 into the equation of our line gives us the final equation y=−3x+6y=-3x+6y=−3x+6.So, the equation of the line parallel to y=−3x+7y=-3x+7y=−3x+7 that goes through the point (1,3)(1,3)(1,3) is y=−3x+6y=-3x+6y=−3x+6.

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QuestionFind the line parallel to $y=-3x+7$ that passes through the point $(1,3)$ .

Assumptions1. The equation of the line we want to find is parallel to $y=-3x+7$ . The line passes through the point $(1,3)$ 3. The slope of a line parallel to another line is the same as the slope of the original line

First, we need to find the slope of the given line. The slope of a line in the form $y=mx+b$ is $m$ .
The given line is $y=-x+7$ , so the slope is $-$ .

Since the line we want to find is parallel to the given line, its slope is also $-3$ .

The equation of a line in slope-intercept form is $y=mx+b$ , where $m$ is the slope and $b$ is the y-intercept. We know the slope of our line is $-3$ , so the equation of our line is $y=-3x+b$ .

To find the y-intercept $b$ , we can use the point $(1,3)$ that the line passes through. Substituting $x=1$ and $y=3$ into the equation gives us $3=-3(1)+b$ .

olving for $b$ gives us $b=3+3=6$ .

Substituting $b=6$ into the equation of our line gives us the final equation $y=-3x+6$ .
So, the equation of the line parallel to $y=-3x+7$ that goes through the point $(1,3)$ is $y=-3x+6$ .