a Given:
The equation of line 1 is given as y = 2x-4.
Another line 2 passes parallel through line 1 and through the point (-7,-11).
Explanation:
The general equation of the slope-intercept form of a line is,
[tex]y=mx+b\text{ . . . . .(1)}[/tex]
By comparing the equation (1) with the equation of line 1,
[tex]m=2[/tex]
Since line 2 is parallel to line 1, the slope of the two lines will be equal.
To find the equation of line 2:
The equation of line using a slope and a point can be calculated as,
[tex]y-y_1=m(x-x_1)\text{ . . .. .(2)}[/tex]
Consider the given point as
[tex](x_1,y_1)=(-7,-11)[/tex]
On plugging the obtained values in equation (2),
[tex]\begin{gathered} y-(-11)=2(x-(-7)) \\ y+11=2(x+7) \end{gathered}[/tex]
The equation of line 2 in the slope-intercept form will be,
[tex]\begin{gathered} y+11=2x+14 \\ y=2x+14-11 \\ y=2x+3 \end{gathered}[/tex]
Hence, the equation of line 2 in the slop-intercept form is y = 2x+3.
