Question

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

Answer 1

The equation of the line given is,

`y=-4x-3`

We were told that a line is parallel to the equation.

Therefore, from the equation above, the slope of the line is

`m_1=-4`

Rule for paralel line

`m_1=m_2`

Hence, the slope (m2) is

`-4`

Also, the line passes through the point (-2,4).

The formula to calculate the equation in sope-intercept dform is,

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

where,

`(x_1,y_1)=(-2,4)`

Therefore,

`y-4=-4(x-(-2))`

Simplify

`\begin{gathered} y-4=-4(x+2) \\ y-4=-4x-8 \\ y=-4x-8+4 \\ y=-4x-4 \end{gathered}`

Hence, the equation of theline is

`y=-4x-4\text{ \lparen Option 3\rparen}`