Find the Equation with a Point and Slope m=-5 , (2,7)

$m = - 5$ , $(2, 7)$

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.

$y = (- 5) \cdot x + b$

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

$7 = (- 5) \cdot (2) + b$

Find the value of $b$ .

Rewrite the equation as $(- 5) \cdot (2) + b = 7$ .

$(- 5) \cdot (2) + b = 7$

Multiply $- 5$ by $2$ .

$- 10 + b = 7$

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

Add $10$ to both sides of the equation.

$b = 7 + 10$

Add $7$ and $10$ .

$b = 17$

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.

$y = - 5 x + 17$

Step 3