Answer:
The intercepts [tex](x,y) = (\frac{3}{2},-2)[/tex]
Step-by-step explanation:
Given:
[tex]4x-1=3y+5[/tex]
Required
Determine the intercepts
The equation is a linear equation and the intercepts of the equation is calculated as thus;
For x intercepts; substitute 0 for y
[tex]4x-1=3y+5[/tex]
[tex]4x-1=3(0)+5[/tex]
[tex]4x-1=0 + 5[/tex]
[tex]4x-1=5[/tex]
Add 1 to both sides
[tex]4x-1 + 1=5 + 1[/tex]
[tex]4x = 6[/tex]
Divide both sides by 4
[tex]\frac{4x}{4} = \frac{6}{4}[/tex]
[tex]x = \frac{6}{4}[/tex]
Simplify fraction to lowest term
[tex]x = \frac{3}{2}[/tex]
For y intercept, substitute 0 for x
[tex]4x-1=3y+5[/tex]
[tex]4(0)-1=3y+5[/tex]
[tex]0 - 1 = 3y + 5[/tex]
[tex]-1 = 3y + 5[/tex]
Subtract 5 from both sides
[tex]-5 - 1 = 3y + 5 - 5[/tex]
[tex]-6 = 3y[/tex]
Divide both sides by 3
[tex]\frac{-6}{3} = \frac{3y}{3}[/tex]
[tex]-2 = y[/tex]
Reorder
[tex]y = -2[/tex]
Hence, the intercepts [tex](x,y) = (\frac{3}{2},-2)[/tex]
