QuestionFind the equation of the line through $(-5,-5)$ , parallel to $y=\frac{2}{5}x+4$ .

Studdy Solution

STEP 1

Assumptions1. We have a line that passes through the point $(-5,-5)$ . . This line is parallel to the line $y=\frac{}{5}x+4$ .

STEP 2

We know that parallel lines have the same slope. Therefore, the slope of the line we are looking for is the same as the slope of the given line, which is $\frac{2}{5}$ .

STEP 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. Since we know the slope of our line, we can write the equation of our line as $y=\frac{2}{5}x+b$ .

STEP 4

To find the y-intercept $b$ , we can substitute the coordinates of the given point $(-,-)$ into the equation.
$-=\frac{2}{}(-)+b$

STEP 5

implify the equation to solve for $b$ .
$-5=-2+b$

STEP 6

Add2 to both sides of the equation to isolate $b$ .
$b=-5+2$

STEP 7

Calculate the value of $b$ .
$b=-3$

STEP 8

Now that we have the y-intercept, we can write the equation of the line that passes through the point $(-5,-5)$ and is parallel to the line $y=\frac{2}{5}x+4$ .
$y=\frac{2}{5}x-3$ This is the equation of the line.

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QuestionFind the equation of the line through $(-5,-5)$ , parallel to $y=\frac{2}{5}x+4$ .

Studdy Solution

STEP 1

Assumptions1. We have a line that passes through the point $(-5,-5)$ . . This line is parallel to the line $y=\frac{}{5}x+4$ .

STEP 2

We know that parallel lines have the same slope. Therefore, the slope of the line we are looking for is the same as the slope of the given line, which is $\frac{2}{5}$ .

STEP 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. Since we know the slope of our line, we can write the equation of our line as $y=\frac{2}{5}x+b$ .

STEP 4

To find the y-intercept $b$ , we can substitute the coordinates of the given point $(-,-)$ into the equation.
$-=\frac{2}{}(-)+b$

STEP 5

implify the equation to solve for $b$ .
$-5=-2+b$

STEP 6

Add2 to both sides of the equation to isolate $b$ .
$b=-5+2$

STEP 7

Calculate the value of $b$ .
$b=-3$

STEP 8

Now that we have the y-intercept, we can write the equation of the line that passes through the point $(-5,-5)$ and is parallel to the line $y=\frac{2}{5}x+4$ .
$y=\frac{2}{5}x-3$ This is the equation of the line.

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QuestionFind the equation of the line through (−5,−5)(-5,-5)(−5,−5), parallel to y=25x+4y=\frac{2}{5}x+4y=52​x+4.

Studdy Solution

STEP 1

Assumptions1. We have a line that passes through the point (−5,−5)(-5,-5)(−5,−5). . This line is parallel to the line y=5x+4y=\frac{}{5}x+4y=5​x+4.

STEP 2

We know that parallel lines have the same slope. Therefore, the slope of the line we are looking for is the same as the slope of the given line, which is 25\frac{2}{5}52​.

STEP 3

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. Since we know the slope of our line, we can write the equation of our line as y=25x+by=\frac{2}{5}x+by=52​x+b.

STEP 4

To find the y-intercept bbb, we can substitute the coordinates of the given point (−,−)(-,-)(−,−) into the equation.−=2(−)+b-=\frac{2}{}(-)+b−=2​(−)+b

STEP 5

implify the equation to solve for bbb.−5=−2+b-5=-2+b−5=−2+b

STEP 6

Add2 to both sides of the equation to isolate bbb.b=−5+2b=-5+2b=−5+2

STEP 7

Calculate the value of bbb.b=−3b=-3b=−3

STEP 8

Now that we have the y-intercept, we can write the equation of the line that passes through the point (−5,−5)(-5,-5)(−5,−5) and is parallel to the line y=25x+4y=\frac{2}{5}x+4y=52​x+4.y=25x−3y=\frac{2}{5}x-3y=52​x−3This is the equation of the line.

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QuestionFind the equation of the line through $(-5,-5)$ , parallel to $y=\frac{2}{5}x+4$ .

Assumptions1. We have a line that passes through the point $(-5,-5)$ . . This line is parallel to the line $y=\frac{}{5}x+4$ .

We know that parallel lines have the same slope. Therefore, the slope of the line we are looking for is the same as the slope of the given line, which is $\frac{2}{5}$ .

The equation of a line in slope-intercept form is $y=mx+b$ , where $m$ is the slope and $b$ is the y-intercept. Since we know the slope of our line, we can write the equation of our line as $y=\frac{2}{5}x+b$ .

To find the y-intercept $b$ , we can substitute the coordinates of the given point $(-,-)$ into the equation.
$-=\frac{2}{}(-)+b$

implify the equation to solve for $b$ .
$-5=-2+b$

Add2 to both sides of the equation to isolate $b$ .
$b=-5+2$

Calculate the value of $b$ .
$b=-3$

Now that we have the y-intercept, we can write the equation of the line that passes through the point $(-5,-5)$ and is parallel to the line $y=\frac{2}{5}x+4$ .
$y=\frac{2}{5}x-3$ This is the equation of the line.