Questions: Graph the linear function by finding x - and y-intercepts. Then write the equation using function notation. -x+3 y=9 Use the graphing tool to graph the equation. Use the intercepts when drawing the line. If only one intercept exists, use it and another point to draw the line. Type the equation using function notation. f(x)=

Graph the linear function by finding x - and y-intercepts. Then write the equation using function notation.

-x+3 y=9

Use the graphing tool to graph the equation. Use the intercepts when drawing the line. If only one intercept exists, use it and another point to draw the line. Type the equation using function notation. f(x)=

Transcript text: Graph the linear function by finding $x$ - and $y$-intercepts. Then write the equation using function notation. \[ -x+3 y=9 \] Use the graphing tool to graph the equation. Use the intercepts when drawing the line. If only one intercept exists, use it and another point to draw the line. Type the equation using function notation. $f(x)=$

Solution

Solution Steps

Step 1: Find the x-intercept

To find the x-intercept, set $ y = 0 $ in the equation $-x + 3y = 9$.

\[ -x + 3(0) = 9 \implies -x = 9 \implies x = -9 \]

The x-intercept is $(-9, 0)$.

Step 2: Find the y-intercept

To find the y-intercept, set $ x = 0 $ in the equation $-x + 3y = 9$.

\[ -(0) + 3y = 9 \implies 3y = 9 \implies y = 3 \]

The y-intercept is $(0, 3)$.

Step 3: Write the equation in function notation

Rearrange the equation $-x + 3y = 9$ to solve for $ y $.

\[ 3y = x + 9 \implies y = \frac{1}{3}x + 3 \]

In function notation, the equation is:

\[ f(x) = \frac{1}{3}x + 3 \]

Final Answer

x-intercept: $(-9, 0)$
y-intercept: $(0, 3)$
Function notation: $ f(x) = \frac{1}{3}x + 3 $

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 1, "ymin": -1, "ymax": 4}, "commands": ["y = (1/3)x + 3"], "latex_expressions": ["$y = \\frac{1}{3}x + 3$"]}

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