QuestionFind the line equation through $(8,1)$ parallel to $y=-\frac{1}{4} x-3$ . Options: A, B, C, D, E.

Studdy Solution

STEP 1

Assumptions1. The line we are looking for is parallel to the line $y=-\frac{1}{4} x-3$ . The line we are looking for passes through the point $(8,1)$ 3. Parallel lines have the same slope

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 $m$ .
$lope = -\frac{1}{4}$

STEP 3

Since the line we are looking for is parallel to the given line, it has the same slope.
$lope_{new} = -\frac{1}{}$

STEP 4

The equation of a line is given by $y=mx+b$ , where $m$ is the slope and $b$ is the y-intercept. We know the slope, and we can find $b$ by plugging in the coordinates of the given point into the equation.
$1 = -\frac{1}{4} \cdot8 + b$

STEP 5

olve for $b$ .
$b =1 +2 =3$

STEP 6

Now that we have the slope and the y-intercept, we can write the equation of the line.
$y = -\frac{1}{4} x +3$ The equation of the line that crosses the point $(8,1)$ and is parallel to the line $y=-\frac{1}{4} x-3$ is $y=-\frac{1}{4} x+3$ .

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QuestionFind the line equation through $(8,1)$ parallel to $y=-\frac{1}{4} x-3$ . Options: A, B, C, D, E.

Studdy Solution

STEP 1

Assumptions1. The line we are looking for is parallel to the line $y=-\frac{1}{4} x-3$ . The line we are looking for passes through the point $(8,1)$ 3. Parallel lines have the same slope

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 $m$ .
$lope = -\frac{1}{4}$

STEP 3

Since the line we are looking for is parallel to the given line, it has the same slope.
$lope_{new} = -\frac{1}{}$

STEP 4

The equation of a line is given by $y=mx+b$ , where $m$ is the slope and $b$ is the y-intercept. We know the slope, and we can find $b$ by plugging in the coordinates of the given point into the equation.
$1 = -\frac{1}{4} \cdot8 + b$

STEP 5

olve for $b$ .
$b =1 +2 =3$

STEP 6

Now that we have the slope and the y-intercept, we can write the equation of the line.
$y = -\frac{1}{4} x +3$ The equation of the line that crosses the point $(8,1)$ and is parallel to the line $y=-\frac{1}{4} x-3$ is $y=-\frac{1}{4} x+3$ .

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QuestionFind the line equation through (8,1)(8,1)(8,1) parallel to y=−14x−3y=-\frac{1}{4} x-3y=−41​x−3. Options: A, B, C, D, E.

Studdy Solution

STEP 1

Assumptions1. The line we are looking for is parallel to the line y=−14x−3y=-\frac{1}{4} x-3y=−41​x−3 . The line we are looking for passes through the point (8,1)(8,1)(8,1)3. Parallel lines have the same slope

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.lope=−14lope = -\frac{1}{4}lope=−41​

STEP 3

Since the line we are looking for is parallel to the given line, it has the same slope.lopenew=−1lope_{new} = -\frac{1}{}lopenew​=−1​

STEP 4

The equation of a line is given by y=mx+by=mx+by=mx+b, where mmm is the slope and bbb is the y-intercept. We know the slope, and we can find bbb by plugging in the coordinates of the given point into the equation.1=−14⋅8+b1 = -\frac{1}{4} \cdot8 + b1=−41​⋅8+b

STEP 5

olve for bbb.b=1+2=3b =1 +2 =3b=1+2=3

STEP 6

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QuestionFind the line equation through $(8,1)$ parallel to $y=-\frac{1}{4} x-3$ . Options: A, B, C, D, E.

Assumptions1. The line we are looking for is parallel to the line $y=-\frac{1}{4} x-3$ . The line we are looking for passes through the point $(8,1)$ 3. Parallel lines have the same slope

First, we need to find the slope of the given line. The slope of a line in the form $y=mx+b$ is $m$ .
$lope = -\frac{1}{4}$

Since the line we are looking for is parallel to the given line, it has the same slope.
$lope_{new} = -\frac{1}{}$

The equation of a line is given by $y=mx+b$ , where $m$ is the slope and $b$ is the y-intercept. We know the slope, and we can find $b$ by plugging in the coordinates of the given point into the equation.
$1 = -\frac{1}{4} \cdot8 + b$

olve for $b$ .
$b =1 +2 =3$