Question

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

Explanation:

Step1: Identify slope and intercept

The equation is \( y = -2x + 4 \). In \( y = mx + b \), \( m = -2 \) (slope) and \( b = 4 \) (y - intercept). So the line crosses the y - axis at \( (0, 4) \).

Step2: Use slope to find another point

Slope \( m=\frac{\text{rise}}{\text{run}}=-2=\frac{-2}{1} \). From \( (0, 4) \), move down 2 units (rise = - 2) and right 1 unit (run = 1) to get the point \( (1, 2) \). We can also move up 2 units and left 1 unit from \( (0, 4) \) to get \( (-1, 6) \).

Step3: Plot the points and draw the line

Plot the points \( (0, 4) \), \( (1, 2) \), \( (-1, 6) \) (or other points found using the slope) on the coordinate plane and draw a straight line through them.

Answer:

To graph \( y=-2x + 4 \):

1. Plot the y - intercept at \( (0, 4) \).
2. Use the slope \( - 2\) (down 2, right 1 or up 2, left 1) to find additional points (e.g., \( (1, 2) \), \( (-1, 6) \)).
3. Draw a straight line through the plotted points.