Find the Equation Using Slope-Intercept Form m=1/4 , (-3,4)

$m = \frac{1}{4}$ , $(- 3, 4)$

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.

$y = (\frac{1}{4}) x + b$

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

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

Find the value of $b$ .

Rewrite the equation as $\frac{1}{4} \cdot - 3 + b = 4$ .

$\frac{1}{4} \cdot - 3 + b = 4$

Simplify each term.

Combine $\frac{1}{4}$ and $- 3$ .

$\frac{- 3}{4} + b = 4$

Move the negative in front of the fraction.

$- \frac{3}{4} + b = 4$

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

Add $\frac{3}{4}$ to both sides of the equation.

$b = 4 + \frac{3}{4}$

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

$b = 4 \cdot \frac{4}{4} + \frac{3}{4}$

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

$b = \frac{4 \cdot 4}{4} + \frac{3}{4}$

Combine the numerators over the common denominator.

$b = \frac{4 \cdot 4 + 3}{4}$

Simplify the numerator.

Multiply $4$ by $4$ .

$b = \frac{16 + 3}{4}$

Add $16$ and $3$ .

$b = \frac{19}{4}$

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.

$y = \frac{1}{4} x + \frac{19}{4}$

Step 3