Question

module 11 (linear equations) assignment
score: 13/20 answered: 13/20
question 14
put in slope intercept form, then give the slope and y-intercept below
5x - 9y = -3
the slope is
the y-intercept is
be sure to write the slope and y-intercept as a fraction or integer. do not enter in a decimal.
submit question

Explanation:

Step1: Recall slope-intercept form

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\)-intercept. We need to rearrange the given equation \(5x-9y=-3\) into this form.
First, isolate the \(y\)-term. Subtract \(5x\) from both sides of the equation:
\(-9y=-5x - 3\)

Step2: Solve for \(y\)

Divide every term in the equation \(-9y=-5x - 3\) by \(-9\) to solve for \(y\):
\(y=\frac{-5x}{-9}+\frac{-3}{-9}\)
Simplify each fraction:
\(y = \frac{5}{9}x+\frac{1}{3}\)

Answer:

The slope is \(\frac{5}{9}\)
The \(y\)-intercept is \(\frac{1}{3}\)