Question

slope intercept form graph the equation for the line. y = mx + b y = 1/4 x + 2

Explanation:

Step1: Identify slope and intercept

The equation is \( y = \frac{1}{4}x + 2 \). Here, slope \( m=\frac{1}{4} \), y - intercept \( b = 2 \).

Step2: Plot the y - intercept

The y - intercept is 2, so plot the point \( (0,2) \) on the y - axis.

Step3: Use slope to find next point

Slope \( m=\frac{\text{rise}}{\text{run}}=\frac{1}{4} \). From \( (0,2) \), rise 1 unit (up) and run 4 units (right) to get the point \( (0 + 4,2+1)=(4,3) \).

Step4: Draw the line

Draw a straight line through the points \( (0,2) \) and \( (4,3) \) (and extend it in both directions).

Answer:

To graph \( y=\frac{1}{4}x + 2 \):

1. Plot \( (0,2) \) (y - intercept).
2. From \( (0,2) \), move up 1, right 4 to plot \( (4,3) \).
3. Draw a line through these points.