To find the line that represents the linear equation [tex]\(-3y = 15 - 4x\)[/tex], let's start by rewriting it in the slope-intercept form [tex]\(y = mx + b\)[/tex].
1. Isolate [tex]\( y \)[/tex] on one side of the equation:
[tex]\[
-3y = 15 - 4x
\][/tex]
2. Divide both sides by [tex]\(-3\)[/tex] to solve for [tex]\(y\)[/tex]:
[tex]\[
y = \frac{15 - 4x}{-3}
\][/tex]
3. Simplify the right-hand side:
[tex]\[
y = \frac{15}{-3} + \frac{-4x}{-3}
\][/tex]
[tex]\[
y = -5 + \frac{4}{3}x
\][/tex]
4. Rewrite the equation in the slope-intercept form [tex]\(y = mx + b\)[/tex]:
[tex]\[
y = \frac{4}{3}x - 5
\][/tex]
So, the equation [tex]\(-3y = 15 - 4x\)[/tex] rewritten in slope-intercept form is:
[tex]\[
y = \frac{4}{3}x - 5
\][/tex]
Next, we identify the slope ([tex]\(m\)[/tex]) and the [tex]\(y\)[/tex]-intercept ([tex]\(b\)[/tex]) from the slope-intercept form [tex]\(y = mx + b\)[/tex].
- The [tex]\(y\)[/tex]-intercept ([tex]\(b\)[/tex]) is:
[tex]\[
-5
\][/tex]
- The slope ([tex]\(m\)[/tex]) is:
[tex]\[
\frac{4}{3}
\][/tex]
Finally, to summarize:
- The equation [tex]\(-3y = 15 - 4x\)[/tex] rewritten in slope-intercept form is:
[tex]\[
y = \frac{4}{3}x - 5
\][/tex]
- The [tex]\(y\)[/tex]-intercept is:
[tex]\[
-5
\][/tex]
- The slope of the line is:
[tex]\[
\frac{4}{3}
\][/tex]
Therefore, the line representing the linear equation [tex]\(-3y = 15 - 4x\)[/tex] is:
[tex]\[
\boxed{y = \frac{4}{3}x - 5}
\][/tex]
