Question

Putting the equations in slope-intercept form changes the system from

Answer 1

Answer:

The lines are parallel.

The slopes are equal.

Answer 2

$15x+9y=36 \rightarrow y=-\frac{5}{3}x+4 \\ \\ 10x + 6y = 36 \rightarrow y=-\frac{5}{3}x+6$

The lines are parallel.

The slopes are equal.

Explanation:

The standard form of the equation of a line is given by the form:

$Ax+By=C \\ \\ \\ Where: \\ \\ A \ is \ a \ positive \ integer \\ \\ B,C \ are \ integers$

On the other hand, the slope-intercept form of the equation of a line is given by the form:

$y=mx+b \\ \\ \\ m:Slope \\ \\ b:y-intercept$

So let's convert each equation from the standard form to the slope-intercept form:

So, for the first equation:

$15x+9y=36 \\ \\ Solving \ for \ y: \\ \\ 9y=-15x+36 \\ \\ y=\frac{-15x+36}{9} \\ \\ y=-\frac{5}{3}x+4$

So, for the second equation:

$10x + 6y = 36 \\ \\ Solving \ for \ y: \\ \\ 6y=-10x+36 \\ \\ y=\frac{-10x+36}{6} \\ \\ y=-\frac{5}{3}x+6$

As you can see both equations have the same slope but different y-intercepts meaning that they are parallel. So these are the correct options:

The lines are parallel.

The slopes are equal.

Learn more:

Graph linear equations: brainly.com/question/13799715

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