Find the Equation with a Point and Slope What is the equation of the line that passes through the point (5,4) and has a slope of 4/5 ?

What is the equation of the line that passes through the point $(5, 4)$ and has a slope of $\frac{4}{5}$ ?

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.

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

Substitute the value of $y$ into the equation.

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

Find the value of $b$ .

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

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

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

$4 + b = 4$

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

Subtract $4$ from both sides of the equation.

$b = 4 - 4$

Subtract $4$ from $4$ .

$b = 0$

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.

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

Step 3