Find the Equation Using Point-Slope Formula m=-2 and (4,1)

$m = - 2$ and $(4, 1)$

Step 1

Use the slope $- 2$ and a given point $(4, 1)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (1) = - 2 \cdot (x - (4))$

Step 2

Simplify the equation and keep it in point-slope form.

$y - 1 = - 2 \cdot (x - 4)$

Step 3

Solve for $y$ .

Simplify $- 2 \cdot (x - 4)$ .

Rewrite.

$y - 1 = 0 + 0 - 2 \cdot (x - 4)$

Simplify by adding zeros.

$y - 1 = - 2 \cdot (x - 4)$

Apply the distributive property.

$y - 1 = - 2 x - 2 \cdot - 4$

Multiply $- 2$ by $- 4$ .

$y - 1 = - 2 x + 8$

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

Add $1$ to both sides of the equation.

$y = - 2 x + 8 + 1$

Add $8$ and $1$ .

$y = - 2 x + 9$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = - 2 x + 9$

Point-slope form:

$y - 1 = - 2 \cdot (x - 4)$

Step 5

Find the Equation Using Point-Slope Formula m=-2 and (4,1)

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