Find the Equation with a Point and Slope -10 (1,4)

$- 10$ $(1, 4)$

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.

$y = (- 10) \cdot x + b$

Substitute the value of $x$ into the equation.

$y = (- 10) \cdot (1) + b$

Substitute the value of $y$ into the equation.

$4 = (- 10) \cdot (1) + b$

Find the value of $b$ .

Rewrite the equation as $(- 10) \cdot (1) + b = 4$ .

$(- 10) \cdot (1) + b = 4$

Multiply $- 10$ by $1$ .

$- 10 + b = 4$

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

Add $10$ to both sides of the equation.

$b = 4 + 10$

Add $4$ and $10$ .

$b = 14$

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.

$y = - 10 x + 14$

Step 3