Answer :
Given the equation of the line:
[tex]2y-2=-2\mleft(4-x\mright)[/tex]Since we asked on the equation of the line that is parallel to the line of equation 2y-2= -2(4-x), the lines must have the same slope since they are said to be parallel.
2y-2= -2(4-x) is in Point-Slope Form, with standard form of:
[tex]y-y_1_{}=m(x-x_1)[/tex]Where,
m = the slope of the line
Therefore, the slope of the lines must be -2.
Let's now find out the equation of the parallel line in Slope-Intercept Form.
Step 1: Substitute m = -2 and x,y = (-15,-2) in y = mx + b to find the y-intercept (b).
[tex]\text{ y = mx + b}[/tex][tex]\text{ -2 = -2(-15) + b}[/tex][tex]\text{ -2 = 30 + b}[/tex][tex]\text{ -2 - 30 = b}[/tex][tex]\text{ -32 = b }\rightarrow\text{ b = -32}[/tex]Step 2: Let's complete the equation. Substitute m = -2 and b = -32 in y = mx + b.
[tex]\text{ y = mx + b}[/tex][tex]\text{ y = (-2)x + (-32)}[/tex][tex]\text{ y = -2x - 32}[/tex]Therefore, the equation of the line parallel to 2y-2= -2(4-x) in Slope-Intercept From is y = -2x - 32.
