Let's find the slope of the line given by the equation:
[tex]\[
-4x + 7 = 2y - 3
\][/tex]
To determine the slope, we need to express the equation in the slope-intercept form, which is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the y-intercept.
Step 1: Move all y terms to one side and all constant terms to the other side.
Starting with the equation:
[tex]\[
-4x + 7 = 2y - 3
\][/tex]
Add 3 to both sides to isolate the terms containing [tex]\( y \)[/tex]:
[tex]\[
-4x + 7 + 3 = 2y
\][/tex]
Simplify the left-hand side:
[tex]\[
-4x + 10 = 2y
\][/tex]
Step 2: Solve for y by isolating it on one side.
To isolate [tex]\( y \)[/tex], divide both sides of the equation by 2:
[tex]\[
-\frac{4x}{2} + \frac{10}{2} = y
\][/tex]
Simplify the equation:
[tex]\[
-2x + 5 = y
\][/tex]
Now, the equation is in the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope.
From the equation [tex]\( y = -2x + 5 \)[/tex], we can see that the slope ([tex]\( m \)[/tex]) of the line is [tex]\( -2 \)[/tex].
Therefore, the slope of the line is:
[tex]\[
\boxed{-2}
\][/tex]
The correct answer is (C) -2.
