Find Any Equation Parallel to the Line y-x=5

$y - x = 5$

Step 1

Choose a point that the parallel line will pass through.

$(0, 0)$

Step 2

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.

$y = m x + b$

Add $x$ to both sides of the equation.

$y = 5 + x$

Reorder $5$ and $x$ .

$y = x + 5$

Step 3

Using the slope-intercept form, the slope is $1$ .

$m = 1$

Step 4

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

Step 5

Use the slope $1$ and a given point $(0, 0)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = 1 \cdot (x - (0))$

Step 6

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

$y + 0 = 1 \cdot (x + 0)$

Step 7

Solve for $y$ .

Add $y$ and $0$ .

$y = 1 \cdot (x + 0)$

Simplify $1 \cdot (x + 0)$ .

Multiply $x + 0$ by $1$ .

$y = x + 0$

Add $x$ and $0$ .

$y = x$

Step 8

Find Any Equation Parallel to the Line y-x=5

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