Question

Write the standard form equation of the line parallel to y = 2x – 1 that contains the point (2,-7)

Answer 1

Answer:

$y=2x+3$

Step-by-step explanation:

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

$y=mx+b$

Using the slope-intercept form, the slope is 2.

$m=2$

So in order for us to find an equation that is parallel, the slopes must be equal. We need to find the parallel line using the point-slope formula.

We use the slope 2 and a given point $(2,7)$ to substitute for x1 and y1 in the point-slope form $y-y^1 = m (x-x^1)$, which is derived from the slope equation: $m=\frac{y2-y1}{x2-x1}$

Now we simplify the equation and keep it in point-slope form.

$y-7=2$  × $(x-2)$

Simplify $2$ × $(x-2)$

$y-7=2x-4$

$Rewrite.~y-7=0+0+2~x~(x-2)$

$Simplify~ by~adding~zeros.~y-7=2 ~x~(x-2)$

$Apply~the~distributive~property.~y-7=2x+2~X~-2$

$Multiply~2~by~-2.~y-7=2x-4$

Last, We move all terms not containing y to the right side of the equation.

Add 7 to both sides of the equation.

$y=2x-4+7$

Add −4 and 7 and your answer will be: $y=2x+3$