Question Find the value of $x$ given the equation of a line $y-y_1 = m(x-x_1)$

Studdy Solution

STEP 1

Assumptions
1. We have the equation of a line in point-slope form: $y - y_1 = m(x - x_1)$ .
2. We are solving for $x$ .
3. $m$ is the slope of the line.
4. $(x_1, y_1)$ is a point on the line.
5. $y$ is the y-coordinate of another point on the line that corresponds to the x-coordinate we are solving for.

STEP 2

Isolate the term containing $x$ on one side of the equation.
$m(x - x_1) = y - y_1$

STEP 3

Distribute the slope $m$ across the parentheses.
$mx - mx_1 = y - y_1$

STEP 4

Add $mx_1$ to both sides of the equation to get terms involving $x$ on one side.
$mx = y - y_1 + mx_1$

STEP 5

Now, isolate $x$ by dividing both sides of the equation by the slope $m$ .
$x = \frac{y - y_1 + mx_1}{m}$

STEP 6

This is the solution for $x$ in terms of $y$ , $y_1$ , $m$ , and $x_1$ .
$x = \frac{y - y_1}{m} + x_1$

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Question Find the value of $x$ given the equation of a line $y-y_1 = m(x-x_1)$

Studdy Solution

STEP 1

STEP 2

Isolate the term containing $x$ on one side of the equation.
$m(x - x_1) = y - y_1$

STEP 3

Distribute the slope $m$ across the parentheses.
$mx - mx_1 = y - y_1$

STEP 4

Add $mx_1$ to both sides of the equation to get terms involving $x$ on one side.
$mx = y - y_1 + mx_1$

STEP 5

Now, isolate $x$ by dividing both sides of the equation by the slope $m$ .
$x = \frac{y - y_1 + mx_1}{m}$

STEP 6

This is the solution for $x$ in terms of $y$ , $y_1$ , $m$ , and $x_1$ .
$x = \frac{y - y_1}{m} + x_1$

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Question Find the value of xxx given the equation of a line y−y1=m(x−x1)y-y_1 = m(x-x_1)y−y1​=m(x−x1​)

Studdy Solution

STEP 1

STEP 2

Isolate the term containing xxx on one side of the equation.m(x−x1)=y−y1m(x - x_1) = y - y_1m(x−x1​)=y−y1​

STEP 3

Distribute the slope mmm across the parentheses.mx−mx1=y−y1mx - mx_1 = y - y_1mx−mx1​=y−y1​

STEP 4

Add mx1mx_1mx1​ to both sides of the equation to get terms involving xxx on one side.mx=y−y1+mx1mx = y - y_1 + mx_1mx=y−y1​+mx1​

STEP 5

Now, isolate xxx by dividing both sides of the equation by the slope mmm.x=y−y1+mx1mx = \frac{y - y_1 + mx_1}{m}x=my−y1​+mx1​​

STEP 6

This is the solution for xxx in terms of yyy, y1y_1y1​, mmm, and x1x_1x1​.x=y−y1m+x1x = \frac{y - y_1}{m} + x_1x=my−y1​​+x1​

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Question Find the value of $x$ given the equation of a line $y-y_1 = m(x-x_1)$

Isolate the term containing $x$ on one side of the equation.
$m(x - x_1) = y - y_1$

Distribute the slope $m$ across the parentheses.
$mx - mx_1 = y - y_1$

Add $mx_1$ to both sides of the equation to get terms involving $x$ on one side.
$mx = y - y_1 + mx_1$

Now, isolate $x$ by dividing both sides of the equation by the slope $m$ .
$x = \frac{y - y_1 + mx_1}{m}$

This is the solution for $x$ in terms of $y$ , $y_1$ , $m$ , and $x_1$ .
$x = \frac{y - y_1}{m} + x_1$