Find the Equation with a Point and Slope What is the equation of the line that passes through the point (1,3) and has a slope of 6 ?

What is the equation of the line that passes through the point $(1, 3)$ and has a slope of $6$ ?

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.

$y = (6) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (6) \cdot (1) + b$

Substitute the value of $y$ into the equation.

$3 = (6) \cdot (1) + b$

Find the value of $b$ .

Rewrite the equation as $(6) \cdot (1) + b = 3$ .

$(6) \cdot (1) + b = 3$

Multiply $6$ by $1$ .

$6 + b = 3$

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

Subtract $6$ from both sides of the equation.

$b = 3 - 6$

Subtract $6$ from $3$ .

$b = - 3$

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.

$y = 6 x - 3$

Step 3