QuestionFind the line equation with slope $m$ through point (4,4). Answer in slope-intercept form: $m=-\frac{2}{3}$ .

Studdy Solution

STEP 1

Assumptions1. The line passes through the point (4,4) . The slope of the line is $-\frac{}{3}$
3. The equation of the line needs to be in slope-intercept form, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 2

We know the slope of the line and a point that the line passes through. We can use these to find the y-intercept, $b$ , of the line. The formula to find the y-intercept when we know the slope and a point $(x1, y1)$ on the line is $b = y1 - m \cdot x1$

STEP 3

Now, plug in the given values for the slope, $m$ , and the point $(x1, y1)$ to calculate the y-intercept, $b$ .
$b = - (-\frac{2}{3}) \cdot$

STEP 4

implify the expression to calculate the y-intercept, $b$ .
$b =4 - (-\frac{8}{3})$

STEP 5

Further simplify the expression to calculate the y-intercept, $b$ .
$b =4 + \frac{8}{3} = \frac{20}{3}$

STEP 6

Now that we have the slope, $m$ , and the y-intercept, $b$ , we can write the equation of the line in slope-intercept form, $y = mx + b$ .
$y = -\frac{2}{3}x + \frac{20}{3}$ The equation of the line with slope $-\frac{2}{3}$ that passes through the point (4,4) is $y = -\frac{2}{3}x + \frac{20}{3}$ .

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QuestionFind the line equation with slope $m$ through point (4,4). Answer in slope-intercept form: $m=-\frac{2}{3}$ .

Studdy Solution

STEP 1

Assumptions1. The line passes through the point (4,4) . The slope of the line is $-\frac{}{3}$
3. The equation of the line needs to be in slope-intercept form, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 2

We know the slope of the line and a point that the line passes through. We can use these to find the y-intercept, $b$ , of the line. The formula to find the y-intercept when we know the slope and a point $(x1, y1)$ on the line is $b = y1 - m \cdot x1$

STEP 3

Now, plug in the given values for the slope, $m$ , and the point $(x1, y1)$ to calculate the y-intercept, $b$ .
$b = - (-\frac{2}{3}) \cdot$

STEP 4

implify the expression to calculate the y-intercept, $b$ .
$b =4 - (-\frac{8}{3})$

STEP 5

Further simplify the expression to calculate the y-intercept, $b$ .
$b =4 + \frac{8}{3} = \frac{20}{3}$

STEP 6

Now that we have the slope, $m$ , and the y-intercept, $b$ , we can write the equation of the line in slope-intercept form, $y = mx + b$ .
$y = -\frac{2}{3}x + \frac{20}{3}$ The equation of the line with slope $-\frac{2}{3}$ that passes through the point (4,4) is $y = -\frac{2}{3}x + \frac{20}{3}$ .

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QuestionFind the line equation with slope mmm through point (4,4). Answer in slope-intercept form: m=−23m=-\frac{2}{3}m=−32​.

Studdy Solution

STEP 1

Assumptions1. The line passes through the point (4,4) . The slope of the line is −3-\frac{}{3}−3​3. The equation of the line needs to be in slope-intercept form, which is y=mx+by = mx + by=mx+b, where mmm is the slope and bbb is the y-intercept.

STEP 2

We know the slope of the line and a point that the line passes through. We can use these to find the y-intercept, bbb, of the line. The formula to find the y-intercept when we know the slope and a point (x1,y1)(x1, y1)(x1,y1) on the line isb=y1−m⋅x1b = y1 - m \cdot x1b=y1−m⋅x1

STEP 3

Now, plug in the given values for the slope, mmm, and the point (x1,y1)(x1, y1)(x1,y1) to calculate the y-intercept, bbb.b=−(−23)⋅b = - (-\frac{2}{3}) \cdotb=−(−32​)⋅

STEP 4

implify the expression to calculate the y-intercept, bbb.b=4−(−83)b =4 - (-\frac{8}{3})b=4−(−38​)

STEP 5

Further simplify the expression to calculate the y-intercept, bbb.b=4+83=203b =4 + \frac{8}{3} = \frac{20}{3}b=4+38​=320​

STEP 6

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QuestionFind the line equation with slope $m$ through point (4,4). Answer in slope-intercept form: $m=-\frac{2}{3}$ .

Assumptions1. The line passes through the point (4,4) . The slope of the line is $-\frac{}{3}$
3. The equation of the line needs to be in slope-intercept form, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

We know the slope of the line and a point that the line passes through. We can use these to find the y-intercept, $b$ , of the line. The formula to find the y-intercept when we know the slope and a point $(x1, y1)$ on the line is $b = y1 - m \cdot x1$

Now, plug in the given values for the slope, $m$ , and the point $(x1, y1)$ to calculate the y-intercept, $b$ .
$b = - (-\frac{2}{3}) \cdot$

implify the expression to calculate the y-intercept, $b$ .
$b =4 - (-\frac{8}{3})$

Further simplify the expression to calculate the y-intercept, $b$ .
$b =4 + \frac{8}{3} = \frac{20}{3}$