Questions: Find the slope and the y-intercept of the line whose equation is given. y = 2/5 x + 5 The slope is 2/5. (Type an integer or a simplified fraction.) The y-intercept is 5. (Type an ordered pair.)

Find the slope and the y-intercept of the line whose equation is given. y = 2/5 x + 5 The slope is 2/5. (Type an integer or a simplified fraction.) The y-intercept is 5. (Type an ordered pair.)
Transcript text: Find the slope and the $y$-intercept of the line whose equation is given. \[ y=\frac{2}{5} x+5 \] The slope is $\frac{2}{5}$. (Type an integer or a simplified fraction.) The $y$-intercept is 5 . (Type an ordered pair.)
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Solution

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Solution Steps

To find the slope and the y-intercept of a line given in the slope-intercept form \( y = mx + b \), identify the coefficient of \( x \) as the slope \( m \) and the constant term as the y-intercept \( b \). The y-intercept is expressed as an ordered pair \((0, b)\).

Step 1: Identify the Slope

The equation of the line is given in the slope-intercept form \( y = \frac{2}{5} x + 5 \). From this equation, we can identify the slope \( m \) as: \[ m = \frac{2}{5} = 0.4 \]

Step 2: Identify the Y-Intercept

The y-intercept \( b \) is the constant term in the equation, which is: \[ b = 5 \] This can be expressed as the ordered pair \( (0, b) \), resulting in: \[ \text{Y-Intercept} = (0, 5) \]

Final Answer

The slope is \( \boxed{0.4} \) and the y-intercept is \( \boxed{(0, 5)} \).

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