Find the Equation with a Point and Slope m=2 , (5,5)

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

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.

$y = (2) \cdot x + b$

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

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

Find the value of $b$ .

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

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

Multiply $2$ by $5$ .

$10 + b = 5$

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

Subtract $10$ from both sides of the equation.

$b = 5 - 10$

Subtract $10$ from $5$ .

$b = - 5$

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.

$y = 2 x - 5$

Step 3