Questions: What is the y-intercept of each equation? a. y=6x+2 y-intercept: b. 10x+5y=30 y-intercept:

What is the y-intercept of each equation? a. y=6x+2 y-intercept: b. 10x+5y=30 y-intercept:
Transcript text: What is the $y$-intercept of each equation? a. $y=6 x+2$ $y$-intercept: $\square$ b. $10 x+5 y=30$ $y$-intercept: $\square$
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Solution

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Solution Steps

To find the $y$-intercept of an equation, we need to determine the value of $y$ when $x=0$.

a. For the equation $y = 6x + 2$, substitute $x = 0$ to find the $y$-intercept.

b. For the equation $10x + 5y = 30$, set $x = 0$ and solve for $y$ to find the $y$-intercept.

Step 1: Find the \( y \)-intercept for \( y = 6x + 2 \)

To find the \( y \)-intercept, set \( x = 0 \) in the equation \( y = 6x + 2 \): \[ y = 6(0) + 2 = 2 \]

Step 2: Find the \( y \)-intercept for \( 10x + 5y = 30 \)

To find the \( y \)-intercept, set \( x = 0 \) in the equation \( 10x + 5y = 30 \) and solve for \( y \): \[ 10(0) + 5y = 30 \implies 5y = 30 \implies y = \frac{30}{5} = 6 \]

Final Answer

a. The \( y \)-intercept of \( y = 6x + 2 \) is \( \boxed{2} \).

b. The \( y \)-intercept of \( 10x + 5y = 30 \) is \( \boxed{6} \).

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