Find the Equation Using Slope-Intercept Form (-3,-5) ; y=-1/4x-10

$(- 3, - 5)$ ; $y = - \frac{1}{4} x - 10$

Step 1

Combine $x$ and $\frac{1}{4}$ .

$y = - \frac{x}{4} - 10$

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.

$y = (- \frac{x}{4} - 10) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (- \frac{- 3}{4} - 10) \cdot (- 3) + b$

Substitute the value of $y$ into the equation.

$- 5 = (- \frac{- 3}{4} - 10) \cdot (- 3) + b$

Find the value of $b$ .

Rewrite the equation as $(- \frac{- 3}{4} - 10) \cdot - 3 + b = - 5$ .

$(- \frac{- 3}{4} - 10) \cdot - 3 + b = - 5$

Simplify each term.

Move the negative in front of the fraction.

$(- - \frac{3}{4} - 10) \cdot - 3 + b = - 5$

Multiply $- - \frac{3}{4}$ .

Multiply $- 1$ by $- 1$ .

$(1 (\frac{3}{4}) - 10) \cdot - 3 + b = - 5$

Multiply $\frac{3}{4}$ by $1$ .

$(\frac{3}{4} - 10) \cdot - 3 + b = - 5$

To write $- 10$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(\frac{3}{4} - 10 \cdot \frac{4}{4}) \cdot - 3 + b = - 5$

Combine $- 10$ and $\frac{4}{4}$ .

$(\frac{3}{4} + \frac{- 10 \cdot 4}{4}) \cdot - 3 + b = - 5$

Combine the numerators over the common denominator.

$\frac{3 - 10 \cdot 4}{4} \cdot - 3 + b = - 5$

Simplify the numerator.

Multiply $- 10$ by $4$ .

$\frac{3 - 40}{4} \cdot - 3 + b = - 5$

Subtract $40$ from $3$ .

$\frac{- 37}{4} \cdot - 3 + b = - 5$

Move the negative in front of the fraction.

$- \frac{37}{4} \cdot - 3 + b = - 5$

Multiply $- \frac{37}{4} \cdot - 3$ .

Multiply $- 3$ by $- 1$ .

$3 (\frac{37}{4}) + b = - 5$

Combine $3$ and $\frac{37}{4}$ .

$\frac{3 \cdot 37}{4} + b = - 5$

Multiply $3$ by $37$ .

$\frac{111}{4} + b = - 5$

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

Subtract $\frac{111}{4}$ from both sides of the equation.

$b = - 5 - \frac{111}{4}$

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$b = - 5 \cdot \frac{4}{4} - \frac{111}{4}$

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

$b = \frac{- 5 \cdot 4}{4} - \frac{111}{4}$

Combine the numerators over the common denominator.

$b = \frac{- 5 \cdot 4 - 111}{4}$

Simplify the numerator.

Multiply $- 5$ by $4$ .

$b = \frac{- 20 - 111}{4}$

Subtract $111$ from $- 20$ .

$b = \frac{- 131}{4}$

Move the negative in front of the fraction.

$b = - \frac{131}{4}$

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.

$y = - \frac{1}{4} x^{2} - 10 x - \frac{131}{4}$

Step 4

Find the Equation Using Slope-Intercept Form (-3,-5) ; y=-1/4x-10

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