Find the Equation Using Point-Slope Formula (-1,4) , m=5/4

$(- 1, 4)$ , $m = \frac{5}{4}$

Step 1

Use the slope $\frac{5}{4}$ and a given point $(- 1, 4)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (4) = \frac{5}{4} \cdot (x - (- 1))$

Step 2

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

$y - 4 = \frac{5}{4} \cdot (x + 1)$

Step 3

Solve for $y$ .

Simplify $\frac{5}{4} \cdot (x + 1)$ .

Rewrite.

$y - 4 = 0 + 0 + \frac{5}{4} \cdot (x + 1)$

Simplify by adding zeros.

$y - 4 = \frac{5}{4} \cdot (x + 1)$

Apply the distributive property.

$y - 4 = \frac{5}{4} x + \frac{5}{4} \cdot 1$

Combine $\frac{5}{4}$ and $x$ .

$y - 4 = \frac{5 x}{4} + \frac{5}{4} \cdot 1$

Multiply $\frac{5}{4}$ by $1$ .

$y - 4 = \frac{5 x}{4} + \frac{5}{4}$

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

Add $4$ to both sides of the equation.

$y = \frac{5 x}{4} + \frac{5}{4} + 4$

To write $4$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = \frac{5 x}{4} + \frac{5}{4} + 4 \cdot \frac{4}{4}$

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

$y = \frac{5 x}{4} + \frac{5}{4} + \frac{4 \cdot 4}{4}$

Combine the numerators over the common denominator.

$y = \frac{5 x}{4} + \frac{5 + 4 \cdot 4}{4}$

Simplify the numerator.

Multiply $4$ by $4$ .

$y = \frac{5 x}{4} + \frac{5 + 16}{4}$

Add $5$ and $16$ .

$y = \frac{5 x}{4} + \frac{21}{4}$

Reorder terms.

$y = \frac{5}{4} x + \frac{21}{4}$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = \frac{5}{4} x + \frac{21}{4}$

Point-slope form:

$y - 4 = \frac{5}{4} \cdot (x + 1)$

Step 5

Find the Equation Using Point-Slope Formula (-1,4) , m=5/4

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