QuestionFind the equation of the line passing through the point $(-4,5)$ with a slope of $m=\frac{1}{2}$ .

Studdy Solution

STEP 1

Assumptions1. The line passes through the point $(-4,5)$ . The slope of the line is $m=1 /$

STEP 2

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

STEP 3

We can substitute the given slope $m=1 /2$ into the equation. $y = \frac{1}{2}x + b$

STEP 4

We know that the line passes through the point $(-4,)$ . We can substitute these values into the equation to solve for $b$ .
$= \frac{1}{2}(-4) + b$

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 $b$ .
$b =7$

STEP 8

Now that we have the value of $b$ , we can write the equation of the line.
$y = \frac{1}{2}x +7$ The equation of the line through $(-4,5)$ with slope $m=1 /2$ is $y = \frac{1}{2}x +7$ .

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QuestionFind the equation of the line passing through the point $(-4,5)$ with a slope of $m=\frac{1}{2}$ .

Studdy Solution

STEP 1

Assumptions1. The line passes through the point $(-4,5)$ . The slope of the line is $m=1 /$

STEP 2

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

STEP 3

We can substitute the given slope $m=1 /2$ into the equation. $y = \frac{1}{2}x + b$

STEP 4

We know that the line passes through the point $(-4,)$ . We can substitute these values into the equation to solve for $b$ .
$= \frac{1}{2}(-4) + b$

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 $b$ .
$b =7$

STEP 8

Now that we have the value of $b$ , we can write the equation of the line.
$y = \frac{1}{2}x +7$ The equation of the line through $(-4,5)$ with slope $m=1 /2$ is $y = \frac{1}{2}x +7$ .

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QuestionFind the equation of the line passing through the point (−4,5)(-4,5)(−4,5) with a slope of m=12m=\frac{1}{2}m=21​.

Studdy Solution

STEP 1

Assumptions1. The line passes through the point (−4,5)(-4,5)(−4,5). The slope of the line is m=1/m=1 /m=1/

STEP 2

We know that 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.

STEP 3

We can substitute the given slope m=1/2m=1 /2m=1/2 into the equation.y=12x+by = \frac{1}{2}x + by=21​x+b

STEP 4

We know that the line passes through the point (−4,)(-4,)(−4,). We can substitute these values into the equation to solve for bbb.=12(−4)+b = \frac{1}{2}(-4) + b=21​(−4)+b

STEP 5

implify the equation to solve for bbb.5=−2+b5 = -2 + b5=−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=7b =7b=7

STEP 8

Now that we have the value of bbb, we can write the equation of the line.y=12x+7y = \frac{1}{2}x +7y=21​x+7The equation of the line through (−4,5)(-4,5)(−4,5) with slope m=1/2m=1 /2m=1/2 is y=12x+7y = \frac{1}{2}x +7y=21​x+7.

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QuestionFind the equation of the line passing through the point $(-4,5)$ with a slope of $m=\frac{1}{2}$ .

Assumptions1. The line passes through the point $(-4,5)$ . The slope of the line is $m=1 /$

We know that 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 can substitute the given slope $m=1 /2$ into the equation. $y = \frac{1}{2}x + b$

We know that the line passes through the point $(-4,)$ . We can substitute these values into the equation to solve for $b$ .
$= \frac{1}{2}(-4) + b$

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 $b$ .
$b =7$

Now that we have the value of $b$ , we can write the equation of the line.
$y = \frac{1}{2}x +7$ The equation of the line through $(-4,5)$ with slope $m=1 /2$ is $y = \frac{1}{2}x +7$ .