Find the Equation with a Point and Slope (3,1) 4

$(3, 1)$ $4$

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.

$y = (4) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (4) \cdot (3) + b$

Substitute the value of $y$ into the equation.

$1 = (4) \cdot (3) + b$

Find the value of $b$ .

Rewrite the equation as $(4) \cdot (3) + b = 1$ .

$(4) \cdot (3) + b = 1$

Multiply $4$ by $3$ .

$12 + b = 1$

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

Subtract $12$ from both sides of the equation.

$b = 1 - 12$

Subtract $12$ from $1$ .

$b = - 11$

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.

$y = 4 x - 11$

Step 3