Find the Parallel Line (4,3) , y=7/4x+1

$(4, 3)$ , $y = \frac{7}{4} x + 1$

Rewrite in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Simplify the right side.

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

$y = \frac{7 x}{4} + 1$

Reorder terms.

$y = \frac{7}{4} x + 1$

Using the slope-intercept form, the slope is $\frac{7}{4}$ .

$m = \frac{7}{4}$

To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.

Use the slope $\frac{7}{4}$ and a given point $(4, 3)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (3) = \frac{7}{4} \cdot (x - (4))$

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

$y - 3 = \frac{7}{4} \cdot (x - 4)$

Solve for $y$ .

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

Rewrite.

$y - 3 = 0 + 0 + \frac{7}{4} \cdot (x - 4)$

Simplify by adding zeros.

$y - 3 = \frac{7}{4} \cdot (x - 4)$

Apply the distributive property.

$y - 3 = \frac{7}{4} x + \frac{7}{4} \cdot - 4$

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

$y - 3 = \frac{7 x}{4} + \frac{7}{4} \cdot - 4$

Cancel the common factor of $4$ .

Factor $4$ out of $- 4$ .

$y - 3 = \frac{7 x}{4} + \frac{7}{4} \cdot (4 (- 1))$

Cancel the common factor.

$y - 3 = \frac{7 x}{4} + \frac{7}{4} \cdot (4 \cdot - 1)$

Rewrite the expression.

$y - 3 = \frac{7 x}{4} + 7 \cdot - 1$

Multiply $7$ by $- 1$ .

$y - 3 = \frac{7 x}{4} - 7$

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

Add $3$ to both sides of the equation.

$y = \frac{7 x}{4} - 7 + 3$

Add $- 7$ and $3$ .

$y = \frac{7 x}{4} - 4$

Reorder terms.

$y = \frac{7}{4} x - 4$

Find the Parallel Line (4,3) , y=7/4x+1

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