Questions: Find the x-intercept of -6x-3y=30 Write your answer in the form (x, 0), no spaces

Transcript text: odule 5 \& 6 Review HW 1. Find the $x$-intercept of \[ -6 x-3 y=30 \] Write your answer in the form $(x, 0)$, no spaces

Solution

Solution Steps

To find the $x$-intercept of the given equation, we need to set $y$ to 0 and solve for $x$. This is because the $x$-intercept is the point where the graph of the equation crosses the $x$-axis, which occurs when $y = 0$.

Solution Approach

Set $y = 0$ in the equation $-6x - 3y = 30$.
Solve the resulting equation for $x$.

Step 1: Set $ y = 0 $

To find the $ x $-intercept of the equation $ -6x - 3y = 30 $, we set $ y = 0 $: \[ -6x - 3(0) = 30 \]

Step 2: Simplify the Equation

This simplifies to: \[ -6x = 30 \]

Step 3: Solve for $ x $

Now, we solve for $ x $ by dividing both sides by $-6$: \[ x = \frac{30}{-6} = -5 \]

Final Answer

The $ x $-intercept is given in the form $ (x, 0) $: \[ \boxed{(-5, 0)} \]

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