Solved on Sep 26, 2023

Solve for the value of $b$ given the linear equation $\frac{y-b}{x-a}=m$ .

STEP 1

Assumptions1. We are given $y$ , $x$ , $a$ , and $m$ . . We are solving for $b$ in the equation $\frac{y-b}{x-a}=m$ .

STEP 2

First, we need to isolate $b$ on one side of the equation. We can do this by multiplying both sides of the equation by $(x-a)$ .
$b(x-a) = y - m(x-a)$

STEP 3

Now, distribute $b$ and $m$ on both sides of the equation.
$bx - ab = y - mx + am$

STEP 4

Next, we need to isolate $b$ on one side of the equation. We can do this by moving $ab$ and $mx$ to the other side of the equation.
$bx = y - mx + am + ab$

STEP 5

Now, we can solve for $b$ by dividing both sides of the equation by $x$ .
$b = \frac{y - mx + am + ab}{x}$

STEP 6

Finally, we simplify the equation by dividing each term on the right side by $x$ .
$b = \frac{y}{x} - m + \frac{am}{x} + \frac{ab}{x}$ So, the solution for $b$ is $b = \frac{y}{x} - m + \frac{am}{x} + \frac{ab}{x}$

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Solve for the value of $b$ given the linear equation $\frac{y-b}{x-a}=m$ .

STEP 1

Assumptions1. We are given $y$ , $x$ , $a$ , and $m$ . . We are solving for $b$ in the equation $\frac{y-b}{x-a}=m$ .

STEP 2

First, we need to isolate $b$ on one side of the equation. We can do this by multiplying both sides of the equation by $(x-a)$ .
$b(x-a) = y - m(x-a)$

STEP 3

Now, distribute $b$ and $m$ on both sides of the equation.
$bx - ab = y - mx + am$

STEP 4

Next, we need to isolate $b$ on one side of the equation. We can do this by moving $ab$ and $mx$ to the other side of the equation.
$bx = y - mx + am + ab$

STEP 5

Now, we can solve for $b$ by dividing both sides of the equation by $x$ .
$b = \frac{y - mx + am + ab}{x}$

STEP 6

Finally, we simplify the equation by dividing each term on the right side by $x$ .
$b = \frac{y}{x} - m + \frac{am}{x} + \frac{ab}{x}$ So, the solution for $b$ is $b = \frac{y}{x} - m + \frac{am}{x} + \frac{ab}{x}$

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Solve for the value of bbb given the linear equation y−bx−a=m\frac{y-b}{x-a}=mx−ay−b​=m.

STEP 1

Assumptions1. We are given yyy, xxx, aaa, and mmm. . We are solving for bbb in the equation y−bx−a=m\frac{y-b}{x-a}=mx−ay−b​=m.

STEP 2

First, we need to isolate bbb on one side of the equation. We can do this by multiplying both sides of the equation by (x−a)(x-a)(x−a).b(x−a)=y−m(x−a)b(x-a) = y - m(x-a)b(x−a)=y−m(x−a)

STEP 3

Now, distribute bbb and mmm on both sides of the equation.bx−ab=y−mx+ambx - ab = y - mx + ambx−ab=y−mx+am

STEP 4

Next, we need to isolate bbb on one side of the equation. We can do this by moving ababab and mxmxmx to the other side of the equation.bx=y−mx+am+abbx = y - mx + am + abbx=y−mx+am+ab

STEP 5

Now, we can solve for bbb by dividing both sides of the equation by xxx.b=y−mx+am+abxb = \frac{y - mx + am + ab}{x}b=xy−mx+am+ab​

STEP 6

Finally, we simplify the equation by dividing each term on the right side by xxx.b=yx−m+amx+abxb = \frac{y}{x} - m + \frac{am}{x} + \frac{ab}{x}b=xy​−m+xam​+xab​So, the solution for bbb isb=yx−m+amx+abxb = \frac{y}{x} - m + \frac{am}{x} + \frac{ab}{x}b=xy​−m+xam​+xab​

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Solve for the value of $b$ given the linear equation $\frac{y-b}{x-a}=m$ .

Assumptions1. We are given $y$ , $x$ , $a$ , and $m$ . . We are solving for $b$ in the equation $\frac{y-b}{x-a}=m$ .

First, we need to isolate $b$ on one side of the equation. We can do this by multiplying both sides of the equation by $(x-a)$ .
$b(x-a) = y - m(x-a)$

Now, distribute $b$ and $m$ on both sides of the equation.
$bx - ab = y - mx + am$

Next, we need to isolate $b$ on one side of the equation. We can do this by moving $ab$ and $mx$ to the other side of the equation.
$bx = y - mx + am + ab$

Now, we can solve for $b$ by dividing both sides of the equation by $x$ .
$b = \frac{y - mx + am + ab}{x}$

Finally, we simplify the equation by dividing each term on the right side by $x$ .
$b = \frac{y}{x} - m + \frac{am}{x} + \frac{ab}{x}$ So, the solution for $b$ is $b = \frac{y}{x} - m + \frac{am}{x} + \frac{ab}{x}$