Question

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find the x-intercept and y-intercept of the graph of the equation 5x + 3y = 15.
x-intercept:
y-intercept:
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Explanation:

Step1: Find x-intercept (set y=0)

To find the x - intercept, we set \( y = 0 \) in the equation \( 5x+3y = 15 \). Substituting \( y = 0 \) into the equation gives us \( 5x+3(0)=15 \), which simplifies to \( 5x=15 \).

Step2: Solve for x

To solve for \( x \), we divide both sides of the equation \( 5x = 15 \) by 5. So, \( x=\frac{15}{5}=3 \).

Step3: Find y-intercept (set x=0)

To find the y - intercept, we set \( x = 0 \) in the equation \( 5x+3y = 15 \). Substituting \( x = 0 \) into the equation gives us \( 5(0)+3y=15 \), which simplifies to \( 3y = 15 \).

Step4: Solve for y

To solve for \( y \), we divide both sides of the equation \( 3y=15 \) by 3. So, \( y = \frac{15}{3}=5 \).

Answer:

x - intercept: \( 3 \)
y - intercept: \( 5 \)