Find the Equation with a Point and Slope m=4/5 , (6,3)

$m = \frac{4}{5}$ , $(6, 3)$

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.

$y = (\frac{4}{5}) x + b$

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

$3 = (\frac{4}{5}) \cdot (6) + b$

Find the value of $b$ .

Rewrite the equation as $\frac{4}{5} \cdot 6 + b = 3$ .

$\frac{4}{5} \cdot 6 + b = 3$

Multiply $\frac{4}{5} \cdot 6$ .

Combine $\frac{4}{5}$ and $6$ .

$\frac{4 \cdot 6}{5} + b = 3$

Multiply $4$ by $6$ .

$\frac{24}{5} + b = 3$

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

Subtract $\frac{24}{5}$ from both sides of the equation.

$b = 3 - \frac{24}{5}$

To write $3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$b = 3 \cdot \frac{5}{5} - \frac{24}{5}$

Combine $3$ and $\frac{5}{5}$ .

$b = \frac{3 \cdot 5}{5} - \frac{24}{5}$

Combine the numerators over the common denominator.

$b = \frac{3 \cdot 5 - 24}{5}$

Simplify the numerator.

Multiply $3$ by $5$ .

$b = \frac{15 - 24}{5}$

Subtract $24$ from $15$ .

$b = \frac{- 9}{5}$

Move the negative in front of the fraction.

$b = - \frac{9}{5}$

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.

$y = \frac{4}{5} x - \frac{9}{5}$

Step 3