Questions: 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: $\square$

Solution

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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