Questions: Use a graphing utility to graph the equation and approximate any x-and y-intercepts. Verify your results algebraically. y=6(x+3)-3 x-intercept (x, y)=( ) y-intercept (x, y)=( )

Use a graphing utility to graph the equation and approximate any x-and y-intercepts. Verify your results algebraically.

y=6(x+3)-3

x-intercept (x, y)=( )
y-intercept (x, y)=( )

Transcript text: Use a graphing utility to graph the equation and approximate any $x$-and $y$-intercepts. Verify your results algebraically. \[ y=6(x+3)-3 \] $x$-intercept $\quad(x, y)=($ $\square$ ) $y$-intercept $\quad(x, y)=($ $\square$ )

Solution

Solution Steps

Step 1: Simplify the Equation

The given equation is: \[ y = 6(x + 3) - 3 \]

First, simplify the equation: \[ y = 6x + 18 - 3 \] \[ y = 6x + 15 \]

Step 2: Find the x-intercept

To find the x-intercept, set $ y = 0 $ and solve for $ x $: \[ 0 = 6x + 15 \] \[ 6x = -15 \] \[ x = -\frac{15}{6} \] \[ x = -2.5 \]

So, the x-intercept is $(-2.5, 0)$.

Step 3: Find the y-intercept

To find the y-intercept, set $ x = 0 $ and solve for $ y $: \[ y = 6(0) + 15 \] \[ y = 15 \]

So, the y-intercept is $(0, 15)$.

Final Answer

x-intercept: $(-2.5, 0)$
y-intercept: $(0, 15)$

{"axisType": 3, "coordSystem": {"xmin": -5, "xmax": 5, "ymin": -5, "ymax": 20}, "commands": ["y = 6x + 15"], "latex_expressions": ["$y = 6(x+3) - 3$"]}

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