[tex]15x+9y=36 \rightarrow y=-\frac{5}{3}x+4 \\ \\ 10x + 6y = 36 \rightarrow y=-\frac{5}{3}x+6[/tex]
The lines are parallel.
The slopes are equal.
The standard form of the equation of a line is given by the form:
[tex]Ax+By=C \\ \\ \\ Where: \\ \\ A \ is \ a \ positive \ integer \\ \\ B,C \ are \ integers[/tex]
On the other hand, the slope-intercept form of the equation of a line is given by the form:
[tex]y=mx+b \\ \\ \\ m:Slope \\ \\ b:y-intercept[/tex]
So let's convert each equation from the standard form to the slope-intercept form:
So, for the first equation:
[tex]15x+9y=36 \\ \\ Solving \ for \ y: \\ \\ 9y=-15x+36 \\ \\ y=\frac{-15x+36}{9} \\ \\ y=-\frac{5}{3}x+4[/tex]
So, for the second equation:
[tex]10x + 6y = 36 \\ \\ Solving \ for \ y: \\ \\ 6y=-10x+36 \\ \\ y=\frac{-10x+36}{6} \\ \\ y=-\frac{5}{3}x+6[/tex]
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.
Graph linear equations: https://brainly.com/question/13799715
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Answer:
The lines are parallel.
The slopes are equal.
