To find the x-intercept and y-intercept of the equation $5x + 3y = 15$, follow these steps:

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1. Standard Form of the Equation

The given equation is already in standard form: $5x + 3y = 15$ In this form, $Ax + By = C$, where $A = 5$, $B = 3$, and $C = 15$.

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2. Find the x-intercept

The x-intercept occurs when $y = 0$. Substituting $y = 0$ into the equation:

$5x + 3(0) = 15$ Simplify: $5x = 15$ Divide both sides by 5: $x = 3$

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

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3. Find the y-intercept

The y-intercept occurs when $x = 0$. Substituting $x = 0$ into the equation:

$5(0) + 3y = 15$ Simplify: $3y = 15$ Divide both sides by 3: $y = 5$

Thus, the y-intercept is: $(0, 5)$

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Final Answer:

• x-intercept: $(3, 0)$
• y-intercept: $(0, 5)$

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Verification:

1. Substituting $x = 3$ and $y = 0$ into $5x + 3y = 15$: $5(3) + 3(0) = 15 \quad \text{True.}$
2. Substituting $x = 0$ and $y = 5$ into $5x + 3y = 15$: $5(0) + 3(5) = 15 \quad \text{True.}$

Everything checks out correctly.

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Related Questions:

1. What is the slope of the line $5x + 3y = 15$?
2. How do you rewrite $5x + 3y = 15$ in slope-intercept form?
3. What are the steps to graph the line $5x + 3y = 15$?
4. How do you find the midpoint between the x-intercept and y-intercept?
5. How do you solve for a point $(x, y)$ that satisfies $5x + 3y = 15$ given $x = 1$?

Tip: In a standard form equation $Ax + By = C$, the x-intercept is found by setting $y = 0$, and the y-intercept is found by setting $x = 0$.