Find the Equation Using Slope-Intercept Form (6,4) ; slope -3/4

$(6, 4)$ ; slope $- \frac{3}{4}$

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.

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

Substitute the value of $x$ into the equation.

$y = (- \frac{3}{4}) \cdot (6) + b$

Substitute the value of $y$ into the equation.

$4 = (- \frac{3}{4}) \cdot (6) + b$

Find the value of $b$ .

Rewrite the equation as $- \frac{3}{4} \cdot 6 + b = 4$ .

$- \frac{3}{4} \cdot 6 + b = 4$

Simplify each term.

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{- 3}{4} \cdot 6 + b = 4$

Factor $2$ out of $4$ .

$\frac{- 3}{2 (2)} \cdot 6 + b = 4$

Factor $2$ out of $6$ .

$\frac{- 3}{2 \cdot 2} \cdot (2 \cdot 3) + b = 4$

Cancel the common factor.

$\frac{- 3}{2 \cdot 2} \cdot (2 \cdot 3) + b = 4$

Rewrite the expression.

$\frac{- 3}{2} \cdot 3 + b = 4$

Combine $\frac{- 3}{2}$ and $3$ .

$\frac{- 3 \cdot 3}{2} + b = 4$

Multiply $- 3$ by $3$ .

$\frac{- 9}{2} + b = 4$

Move the negative in front of the fraction.

$- \frac{9}{2} + b = 4$

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

Add $\frac{9}{2}$ to both sides of the equation.

$b = 4 + \frac{9}{2}$

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$b = 4 \cdot \frac{2}{2} + \frac{9}{2}$

Combine $4$ and $\frac{2}{2}$ .

$b = \frac{4 \cdot 2}{2} + \frac{9}{2}$

Combine the numerators over the common denominator.

$b = \frac{4 \cdot 2 + 9}{2}$

Simplify the numerator.

Multiply $4$ by $2$ .

$b = \frac{8 + 9}{2}$

Add $8$ and $9$ .

$b = \frac{17}{2}$

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.

$y = - \frac{3}{4} x + \frac{17}{2}$

Find the Equation Using Slope-Intercept Form (6,4) ; slope -3/4

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