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Which line represents the linear equation
[tex]\[ -3y = 15 - 4x? \][/tex]

The equation [tex]\(-3y = 15 - 4x\)[/tex] rewritten in slope-intercept form is [tex]\(\square\)[/tex].

The [tex]\(y\)[/tex]-intercept is [tex]\(\square\)[/tex] and the slope of the line is [tex]\(\square\)[/tex].

Line [tex]\(\square\)[/tex] is the graph of the line [tex]\(-3y = 15 - 4x\)[/tex].


Sagot :

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].