Find the Equation Using Point-Slope Formula (-4,4) y=-7/4x+2

$(- 4, 4)$ $y = - \frac{7}{4} x + 2$

Use the slope $- \frac{7}{4} x + 2$ and a given point $(- 4, 4)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (4) = (- \frac{7}{4} x + 2) \cdot (x - (- 4))$

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

$y - 4 = (- \frac{7}{4} x + 2) \cdot (x + 4)$

Solve for $y$ .

Simplify $(- \frac{7}{4} x + 2) \cdot (x + 4)$ .

Rewrite.

$y - 4 = 0 + 0 + (- \frac{7}{4} x + 2) \cdot (x + 4)$

Simplify each term.

Combine $x$ and $\frac{7}{4}$ .

$y - 4 = (- \frac{x \cdot 7}{4} + 2) \cdot (x + 4)$

Move $7$ to the left of $x$ .

$y - 4 = (- \frac{7 x}{4} + 2) \cdot (x + 4)$

Expand $(- \frac{7 x}{4} + 2) (x + 4)$ using the FOIL Method.

Apply the distributive property.

$y - 4 = - \frac{7 x}{4} (x + 4) + 2 (x + 4)$

Apply the distributive property.

$y - 4 = - \frac{7 x}{4} x - \frac{7 x}{4} \cdot 4 + 2 (x + 4)$

Apply the distributive property.

$y - 4 = - \frac{7 x}{4} x - \frac{7 x}{4} \cdot 4 + 2 x + 2 \cdot 4$

Simplify and combine like terms.

Simplify each term.

Multiply $- \frac{7 x}{4} x$ .

Combine $x$ and $\frac{7 x}{4}$ .

$y - 4 = - \frac{x (7 x)}{4} - \frac{7 x}{4} \cdot 4 + 2 x + 2 \cdot 4$

Raise $x$ to the power of $1$ .

$y - 4 = - \frac{7 (x^{1} x)}{4} - \frac{7 x}{4} \cdot 4 + 2 x + 2 \cdot 4$

Raise $x$ to the power of $1$ .

$y - 4 = - \frac{7 (x^{1} x^{1})}{4} - \frac{7 x}{4} \cdot 4 + 2 x + 2 \cdot 4$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y - 4 = - \frac{7 x^{1 + 1}}{4} - \frac{7 x}{4} \cdot 4 + 2 x + 2 \cdot 4$

Add $1$ and $1$ .

$y - 4 = - \frac{7 x^{2}}{4} - \frac{7 x}{4} \cdot 4 + 2 x + 2 \cdot 4$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{7 x}{4}$ into the numerator.

$y - 4 = - \frac{7 x^{2}}{4} + \frac{- 7 x}{4} \cdot 4 + 2 x + 2 \cdot 4$

Cancel the common factor.

$y - 4 = - \frac{7 x^{2}}{4} + \frac{- 7 x}{4} \cdot 4 + 2 x + 2 \cdot 4$

Rewrite the expression.

$y - 4 = - \frac{7 x^{2}}{4} - 7 x + 2 x + 2 \cdot 4$

Multiply $2$ by $4$ .

$y - 4 = - \frac{7 x^{2}}{4} - 7 x + 2 x + 8$

Add $- 7 x$ and $2 x$ .

$y - 4 = - \frac{7 x^{2}}{4} - 5 x + 8$

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

Add $4$ to both sides of the equation.

$y = - \frac{7 x^{2}}{4} - 5 x + 8 + 4$

Add $8$ and $4$ .

$y = - \frac{7 x^{2}}{4} - 5 x + 12$

List the equation in different forms.

Slope-intercept form:

$y = - \frac{7 x^{2}}{4} - 5 x + 12$

Point-slope form:

$y - 4 = (- \frac{7}{4} x + 2) \cdot (x + 4)$

Find the Equation Using Point-Slope Formula (-4,4) y=-7/4x+2

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