Questions: Consider the following linear equation. [ y=frac32 x+4 ] Step 1 of 2: Determine the slope and the y-intercept (entered as an ordered pair) of the equation above. Reduce all fractions to lowest terms.

Consider the following linear equation. [ y=frac32 x+4 ] Step 1 of 2: Determine the slope and the y-intercept (entered as an ordered pair) of the equation above. Reduce all fractions to lowest terms.
Transcript text: Consider the following linear equation. \[ y=\frac{3}{2} x+4 \] Step 1 of 2: Determine the slope and the $y$-intercept (entered as an ordered pair) of the equation above. Reduce all fractions to lowest terms.
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Solution

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Solution Steps

Step 1: Identify the Slope

The given linear equation is

\[ y = \frac{3}{2} x + 4 \]

In the slope-intercept form \( y = mx + b \), the coefficient of \( x \) represents the slope \( m \). Thus, we have:

\[ m = \frac{3}{2} = 1.5 \]

Step 2: Identify the Y-Intercept

The constant term in the equation represents the y-intercept \( b \). From the equation, we see that:

\[ b = 4 \]

The y-intercept can be expressed as the ordered pair \( (0, b) \):

\[ \text{y-intercept} = (0, 4) \]

Final Answer

The slope is \( \frac{3}{2} \) and the y-intercept is \( (0, 4) \). Therefore, the final answer is:

\[ \boxed{\text{slope} = \frac{3}{2}, \text{y-intercept} = (0, 4)} \]

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