Find the Equation Using Slope-Intercept Form m=3 , (5,2)

$m = 3$ , $(5, 2)$

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.

$y = (3) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (3) \cdot (5) + b$

Substitute the value of $y$ into the equation.

$2 = (3) \cdot (5) + b$

Find the value of $b$ .

Rewrite the equation as $(3) \cdot (5) + b = 2$ .

$(3) \cdot (5) + b = 2$

Multiply $3$ by $5$ .

$15 + b = 2$

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

Subtract $15$ from both sides of the equation.

$b = 2 - 15$

Subtract $15$ from $2$ .

$b = - 13$

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.

$y = 3 x - 13$

Step 3