The equation of a line in the slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
To solve this question, follow the steps below.
Step 01: Write the given equation in the slope-intercept form.
Given:
[tex]4y-7=-2(4-2x)[/tex]
First, use the distributive property of multiplication:
[tex]\begin{gathered} 4y-7=-2*4+(-2)*(-2x) \\ 4y-7=-8+4x \\ 4y-7=-8+4x \end{gathered}[/tex]
Add 7 to both sides.
[tex]\begin{gathered} 4y-7+7=-8+4x+7 \\ 4y=-1+4x \end{gathered}[/tex]
Divide both sides by 4:
[tex]\begin{gathered} \frac{4y}{4}=\frac{4x-1}{4} \\ y=x-\frac{1}{4} \end{gathered}[/tex]
Step 02: Find the slope of the second equation.
Given the lines are parallel, they have the same slope.
Thus, the slope is 1.
Then, the equation of the line is:
[tex]\begin{gathered} y=1*x+b \\ y=x+b \end{gathered}[/tex]
Step 03: Use the given point to find b.
Given the point (12, 6), substitute it in the equation to find b:
[tex]6=12+b[/tex]
Subtracting 12 from both sides:
[tex]\begin{gathered} 6-12=b+12-12 \\ -6=b \\ b=-6 \end{gathered}[/tex]
Thus, the equation of the line is:
[tex]y=x-6[/tex]
Answer:
y = x - 6
