Answer:
x = [tex](-\frac{13}{2} ,0)[/tex] y = (0,26)
Step-by-step explanation:
First find the x intercept
To find the x intercept, substitute 0 for y and solve for x.
[tex](0)-6=4(x+5)[/tex]
Rewrite the equation as [tex]4(x+5)=(0)-6[/tex]
[tex]4(x+5)=(0)-6[/tex]
Subtract 6 from 0.
[tex]4(x+5)=-6[/tex]
Divide each term in [tex]4(x+5)=-6[/tex] by 4.
[tex]\frac{4(x+5)}{4} =\frac{-6}{4}[/tex]
Cancel the common factor of 4.
[tex]x+5=\frac{-6}{4}[/tex]
Simplify [tex]\frac{-6}{4}[/tex]
[tex]x+5=-\frac{3}{2}[/tex]
Subtract 5 from both sides of the equation.
[tex]x=-\frac{3}{2} -5[/tex]
To write [tex]-5[/tex] as a fraction with a common denominator, multiply by [tex]\frac{2}{2}[/tex]
[tex]x=-\frac{3}{2}-5[/tex] · [tex]\frac{2}{2}[/tex]
Combine [tex]-5[/tex] and [tex]\frac{2}{2}[/tex].
[tex]x=-\frac{3}{2} +\frac{-5*2}{2}[/tex]
Combine the numerators over the common denominator.
[tex]x=\frac{-3-5*2}{2}[/tex]
Simplify the numerator.
[tex]x=\frac{-13}{2}[/tex]
Move the negative in front of the fraction.
[tex]x=-\frac{13}{2}[/tex]
x = [tex](-\frac{13}{2} ,0)[/tex]
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Find the y-intercepts.
To find the y-intercept(s), substitute in 0 for x and solve for y.
[tex]y-6=4((0)+5)[/tex]
Add 0 and 5.
[tex]y-6=4 *5[/tex]
Multiply 4 by 5.
[tex]y-6=20[/tex]
Add 6 to both sides of the equation.
[tex]y=20+6[/tex]
Add 20 and 6.
[tex]y=26[/tex]
y = (0, 26)
