Answer:
x-intercept: [tex](-\frac{3}{2},0)[/tex]
y-intercept: [tex](0,\frac{9}{5})[/tex]
Explanation:
We have the following Line equation:
[tex]-6x+5y=9[/tex]
If we want to find the x-intercept (the point where the line crosses with the x-axis), we have to set [tex]y=0[/tex]:
[tex]-6x+5(0)=9[/tex]
[tex]-6x=9[/tex]
[tex]x=-\frac{9}{6}[/tex]
Simplifying:
[tex]x=-\frac{3}{2}[/tex]
Hence, the x-intercept point is [tex](-\frac{3}{2},0)[/tex]
If we want to find the y-intercept (the point where the line crosses with the y-axis), we have to set [tex]x=0[/tex]:
[tex]-6(0)+5y=9[/tex]
[tex]5y=9[/tex]
[tex]y=\frac{9}{5}[/tex]
Hence, the x-intercept point is [tex](0,\frac{9}{5})[/tex]
