Answer:
(6, 0)
Step-by-step explanation:
Given linear equation:
[tex]y=-\dfrac{3}{2}x+9[/tex]
The x-intercept is the point at which the line crosses the x-axis, so when y=0. Therefore, to find the x-intercept of the given line, substitute y=0 and solve for x.
[tex]\textsf{Substitute $y = 0$}:[/tex]
[tex]\implies -\dfrac{3}{2}x+9=0[/tex]
[tex]\textsf{Subtract $9$ from both sides}:[/tex]
[tex]\implies -\dfrac{3}{2}x+9-9=0-9[/tex]
[tex]\implies -\dfrac{3}{2}x=-9[/tex]
[tex]\textsf{Multiply both sides by $2$}:[/tex]
[tex]\implies -\dfrac{3}{2}x \cdot 2=-9 \cdot 2[/tex]
[tex]\implies -3x=-18[/tex]
[tex]\textsf{Divide both sides by $-3$}:[/tex]
[tex]\implies \dfrac{-3x}{-3}=\dfrac{-18}{-3}[/tex]
[tex]\implies x=6[/tex]
Therefore the x-intercept of the given line is (6, 0).
