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

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

`y=2x+7`

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* x)+(2* 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`