Find the Equation Using Point-Slope Formula (4,2) , slope=3

$(4, 2)$ , $s l o p e = 3$

Step 1

Use the slope $3$ and a given point $(4, 2)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (2) = 3 \cdot (x - (4))$

Step 2

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

$y - 2 = 3 \cdot (x - 4)$

Step 3

Solve for $y$ .

Simplify $3 \cdot (x - 4)$ .

Rewrite.

$y - 2 = 0 + 0 + 3 \cdot (x - 4)$

Simplify by adding zeros.

$y - 2 = 3 \cdot (x - 4)$

Apply the distributive property.

$y - 2 = 3 x + 3 \cdot - 4$

Multiply $3$ by $- 4$ .

$y - 2 = 3 x - 12$

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

Add $2$ to both sides of the equation.

$y = 3 x - 12 + 2$

Add $- 12$ and $2$ .

$y = 3 x - 10$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = 3 x - 10$

Point-slope form:

$y - 2 = 3 \cdot (x - 4)$

Step 5

Find the Equation Using Point-Slope Formula (4,2) , slope=3

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