Answer:
The Correct option is Last one [tex]y=-4x-4[/tex]
Therefore, equation of the line in slope-intercept that passes through (-2,4) and is parallel to the line [tex]y=-4x-3[/tex] is [tex]y=-4x-4[/tex]
Step-by-step explanation:
Given:
[tex]y=-4x-3[/tex]
To Find:
Equation of line passing through ( -2, 4) and is parallel to the line y=-4x-3
Solution:
[tex]y=-4x-3[/tex] ..........Given
Comparing with Slope-Intercept form,
[tex]y=mx+c[/tex]
Where m =slope
We get
[tex]Slope = m = -4[/tex]
We know that parallel lines have Equal slopes.
Therefore the slope of the required line passing through (-2 , 4) will also have the slope = m = -4.
Now the equation of line in slope point form given by
[tex](y-y_{1})=m(x-x_{1})[/tex]
Substituting the points and so we will get the required equation of the line,
[tex](y-4))=-4(x-(-2))=-4x-8\\\\y=-4x-8+4=-4x-4\\\\y=-4x-4......Equation\ of\ line[/tex]
Therefore, equation of the line in slope-intercept that passes through (-2,4) and is parallel to the line [tex]y=-4x-3[/tex] is [tex]y=-4x-4[/tex]
