Questions: Find the x-and y-intercepts. 6x-9y=18 x-intercept (x, y)=( ) y-intercept (x, y)=( ) Use the intercepts to graph the equation.

Transcript text: Find the $x$-and $y$-intercepts. \[ 6 x-9 y=18 \] $x$-intercept $\quad(x, y)=($ $\square$ ) $y$-intercept $\quad(x, y)=($ $\square$ ) Use the intercepts to graph the equation.

Solution

Solution Steps

Step 1: Find the x-intercept

To find the x-intercept, set $ y = 0 $ in the equation $ 6x - 9y = 18 $.

\[ 6x - 9(0) = 18 \implies 6x = 18 \implies x = \frac{18}{6} = 3 \]

Thus, the x-intercept is $(3, 0)$.

Step 2: Find the y-intercept

To find the y-intercept, set $ x = 0 $ in the equation $ 6x - 9y = 18 $.

\[ 6(0) - 9y = 18 \implies -9y = 18 \implies y = \frac{18}{-9} = -2 \]

Thus, the y-intercept is $(0, -2)$.

Final Answer

x-intercept: $(3, 0)$
y-intercept: $(0, -2)$

{"axisType": 3, "coordSystem": {"xmin": -1, "xmax": 4, "ymin": -3, "ymax": 1}, "commands": ["y = (2/3)x - 2"], "latex_expressions": ["$6x - 9y = 18$"]}

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