Question

write an equation in slop-intercept form for the line that passes through (-3,1) and is parallel to y=2x-4

Answer 1

Answer:

The equation of line in slop-intercept form is given by:

$y=2x+7$

Step-by-step explanation:

Given equation of line:

$y=2x-4$

To find the equation of line parallel to the line of the given equation and passes through point (-3,1).

Applying slope relationship between perpendicular lines.

$m_1=m_2$

where $m_1$ and $m_2$ are slopes of parallel lines.

For the given equation in the form $y=mx+b$ the slope $m_2$ can be found by comparing $y=2x-4$ with standard form.

∴ $m_2=2$

Thus slope of line parallel to this line $m_1$ would be given as:

∴ $m_1=2$

The line passes through point (-3,1)

Using point slope form:

$y-y_1=m(x-x_1)$

Where $(x_1,y_1)\rightarrow (-3,1)$ and $m=m_2=2$

So,

$y-1=2(x-(-3))$

$y-1=2(x+3)$

Using distribution.

$y-1=(2\times x)+(2\times 3)$

$y-1=2x+6$

Adding 1 to both sides.

$y-1+1=2x+6+1$

$y=2x+7$

Thus the equation of line in slop-intercept form is given by:

$y=2x+7$