Find the Equation with a Point and Slope (-10,-6) ; m=-5/8

$(- 10, - 6)$ ; $m = - \frac{5}{8}$

Step 1

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.

$y = (- \frac{5}{8}) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (- \frac{5}{8}) \cdot (- 10) + b$

Substitute the value of $y$ into the equation.

$- 6 = (- \frac{5}{8}) \cdot (- 10) + b$

Find the value of $b$ .

Rewrite the equation as $- \frac{5}{8} \cdot - 10 + b = - 6$ .

$- \frac{5}{8} \cdot - 10 + b = - 6$

Simplify each term.

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{5}{8}$ into the numerator.

$\frac{- 5}{8} \cdot - 10 + b = - 6$

Factor $2$ out of $8$ .

$\frac{- 5}{2 (4)} \cdot - 10 + b = - 6$

Factor $2$ out of $- 10$ .

$\frac{- 5}{2 \cdot 4} \cdot (2 \cdot - 5) + b = - 6$

Cancel the common factor.

$\frac{- 5}{2 \cdot 4} \cdot (2 \cdot - 5) + b = - 6$

Rewrite the expression.

$\frac{- 5}{4} \cdot - 5 + b = - 6$

Combine $\frac{- 5}{4}$ and $- 5$ .

$\frac{- 5 \cdot - 5}{4} + b = - 6$

Multiply $- 5$ by $- 5$ .

$\frac{25}{4} + b = - 6$

Move all terms not containing $b$ to the right side of the equation.

Subtract $\frac{25}{4}$ from both sides of the equation.

$b = - 6 - \frac{25}{4}$

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$b = - 6 \cdot \frac{4}{4} - \frac{25}{4}$

Combine $- 6$ and $\frac{4}{4}$ .

$b = \frac{- 6 \cdot 4}{4} - \frac{25}{4}$

Combine the numerators over the common denominator.

$b = \frac{- 6 \cdot 4 - 25}{4}$

Simplify the numerator.

Multiply $- 6$ by $4$ .

$b = \frac{- 24 - 25}{4}$

Subtract $25$ from $- 24$ .

$b = \frac{- 49}{4}$

Move the negative in front of the fraction.

$b = - \frac{49}{4}$

Step 2

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.

$y = - \frac{5}{8} x - \frac{49}{4}$

Step 3

Find the Equation with a Point and Slope (-10,-6) ; m=-5/8

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