Respuesta :
ANSWER:
Perpendicular
STEP-BY-STEP EXPLANATION:
We have the following equations
[tex]\begin{gathered} 4x+3y=9 \\ 6x-8y=20 \end{gathered}[/tex]We can determine their relationship by means of the slope, since if the slope is equal they are parallels or if the product of it is equal to -1 they are perpendicular.
Therefore we must calculate the slope of each equation
The equation in its slope-intercept form is as follows:
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope } \end{gathered}[/tex]Now, for each equation we solve for y, thus we calculate its slope:
[tex]\begin{gathered} 4x+3y=9\rightarrow y=\frac{9-4x}{3}\rightarrow y=-\frac{4}{3}x+3 \\ m=-\frac{4}{3} \\ 6x-8y=20\rightarrow y=\frac{20-6x}{-8}\rightarrow y=\frac{3}{4}x-\frac{5}{2} \\ m=\frac{3}{4} \end{gathered}[/tex]Now, we rerify the relationship between the slopes:
[tex]-\frac{4}{3}\cdot\frac{3}{4}=-1[/tex]Which means that these equations are perpendicular
