To convert the given equation [tex]\( 4x - 3y = 24 \)[/tex] to slope-intercept form, which is in the form [tex]\( y = mx + b \)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
4x - 3y = 24
\][/tex]
2. Isolate the term involving [tex]\( y \)[/tex] on one side of the equation. To do this, move [tex]\( 4x \)[/tex] to the other side:
[tex]\[
-3y = -4x + 24
\][/tex]
3. Solve for [tex]\( y \)[/tex] by dividing every term by [tex]\(-3\)[/tex] to get [tex]\( y \)[/tex] by itself:
[tex]\[
y = \frac{-4x + 24}{-3}
\][/tex]
4. Simplify the division:
[tex]\[
y = \frac{-4}{-3}x + \frac{24}{-3}
\][/tex]
Which simplifies to:
[tex]\[
y = \frac{4}{3}x - 8
\][/tex]
Thus, the slope-intercept form of the equation [tex]\( 4x - 3y = 24 \)[/tex] is:
[tex]\[
y = \frac{4}{3}x - 8
\][/tex]
Now, let's identify this form among the given options:
- [tex]\( y = \frac{4}{3}x - 8 \)[/tex]
- [tex]\( y = -\frac{4}{3}x + 8 \)[/tex] (not equivalent)
- [tex]\( y = \frac{4}{3}x - 24 \)[/tex] (wrong constant term)
- [tex]\( y = -\frac{4}{3}x + 24 \)[/tex] (not equivalent)
Therefore, the correct slope-intercept form of the equation [tex]\( 4x - 3y = 24 \)[/tex] is:
[tex]\[
y = \frac{4}{3}x - 8
\][/tex]
This matches the first given option.
