Write in Slope-Intercept Form (-2,-3) , slope=5/2

$(- 2, - 3)$ , $s l o p e = \frac{5}{2}$

Step 1

Divide each term in $s l o p e = \frac{5}{2}$ by $l o p e$ and simplify.

Divide each term in $s l o p e = \frac{5}{2}$ by $l o p e$ .

$\frac{s l o p e}{l o p e} = \frac{\frac{5}{2}}{l o p e}$

Simplify the left side.

Cancel the common factor of $l$ .

Cancel the common factor.

$\frac{s l o p e}{l o p e} = \frac{\frac{5}{2}}{l o p e}$

Rewrite the expression.

$\frac{s o p e}{o p e} = \frac{\frac{5}{2}}{l o p e}$

Cancel the common factor of $o$ .

Cancel the common factor.

$\frac{s o p e}{o p e} = \frac{\frac{5}{2}}{l o p e}$

Rewrite the expression.

$\frac{s p e}{p e} = \frac{\frac{5}{2}}{l o p e}$

Cancel the common factor of $p$ .

Cancel the common factor.

$\frac{s p e}{p e} = \frac{\frac{5}{2}}{l o p e}$

Rewrite the expression.

$\frac{s e}{e} = \frac{\frac{5}{2}}{l o p e}$

Cancel the common factor of $e$ .

Cancel the common factor.

$\frac{s e}{e} = \frac{\frac{5}{2}}{l o p e}$

Divide $s$ by $1$ .

$s = \frac{\frac{5}{2}}{l o p e}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$s = \frac{5}{2} \cdot \frac{1}{l o p e}$

Multiply $\frac{5}{2}$ by $\frac{1}{l o p e}$ .

$s = \frac{5}{2 l o p e}$

Step 2

Find the value of $b$ using the formula for the equation of a line.

Use the formula for the equation of a line to find $b$ .

$y = m x + b$

Substitute the value of $m$ into the equation.

$y = (\frac{5}{2 l o p e}) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (\frac{5}{2 l o p e}) \cdot (- 2) + b$

Substitute the value of $y$ into the equation.

$- 3 = (\frac{5}{2 l o p e}) \cdot (- 2) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{5}{2 l o p e} \cdot - 2 + b = - 3$ .

$\frac{5}{2 l o p e} \cdot - 2 + b = - 3$

Simplify each term.

Cancel the common factor of $2$ .

Factor $2$ out of $2 l o p e$ .

$\frac{5}{2 (l o p e)} \cdot - 2 + b = - 3$

Factor $2$ out of $- 2$ .

$\frac{5}{2 (l o p e)} \cdot (2 (- 1)) + b = - 3$

Cancel the common factor.

$\frac{5}{2 (l o p e)} \cdot (2 \cdot - 1) + b = - 3$

Rewrite the expression.

$\frac{5}{l o p e} \cdot - 1 + b = - 3$

Combine $\frac{5}{l o p e}$ and $- 1$ .

$\frac{5 \cdot - 1}{l o p e} + b = - 3$

Multiply $5$ by $- 1$ .

$\frac{- 5}{l o p e} + b = - 3$

Move the negative in front of the fraction.

$- \frac{5}{l o p e} + b = - 3$

Add $\frac{5}{l o p e}$ to both sides of the equation.

$b = - 3 + \frac{5}{l o p e}$

Step 3

Now that the values of $m$ (slope) and $b$ (y-intercept) are known, substitute them into $y = m x + b$ to find the equation of the line.

$y = \frac{5 x}{2 l o p e} - 3 + \frac{5}{l o p e}$

Step 4

Write in Slope-Intercept Form (-2,-3) , slope=5/2

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