To find the equation of the line [tex]\( -3y = 15 - 4x \)[/tex] in slope-intercept form, follow these steps:
1. Isolate [tex]\(y\)[/tex]:
Given: [tex]\( -3y = 15 - 4x \)[/tex]
Divide both sides by [tex]\(-3\)[/tex] to solve for [tex]\(y\)[/tex]:
[tex]\[
y = -\frac{15}{-3} + \frac{4}{-3}x
\][/tex]
Simplifying, we get:
[tex]\[
y = 5 - \frac{4}{3}x
\][/tex]
2. Write in slope-intercept form:
Slope-intercept form is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
Rearrange the equation to match this form:
[tex]\[
y = -\frac{4}{3}x + 5
\][/tex]
Thus, the equation [tex]\( -3y = 15 - 4x \)[/tex] rewritten in slope-intercept form is [tex]\(\boxed{y = -\frac{4}{3}x + 5}\)[/tex].
The y-intercept is the constant term "b" in the slope-intercept form, which here is [tex]\(\boxed{5}\)[/tex].
The slope is the coefficient of [tex]\(x\)[/tex], which in this case is [tex]\(\boxed{-\frac{4}{3}}\)[/tex].
So, line [tex]\(\boxed{y = -\frac{4}{3}x + 5}\)[/tex] is the graph of the line [tex]\( -3y = 15 - 4x \)[/tex].
