Question

graph the line. y = -5x + 2

Explanation:

Step1: Identify slope and y-intercept

The equation is \( y = -5x + 2 \), which is in slope - intercept form \( y=mx + b \), where \( m=-5 \) (slope) and \( b = 2 \) (y - intercept).

Step2: Plot the y-intercept

The y - intercept is \( b = 2 \), so we plot the point \( (0,2) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m=-5=\frac{- 5}{1}\). From the point \( (0,2) \), we move down 5 units (because the numerator of the slope is - 5, which represents a change in y) and then move 1 unit to the right (because the denominator of the slope is 1, which represents a change in x). This gives us the point \( (0 + 1,2-5)=(1,-3) \). We can also move up 5 units and left 1 unit from \( (0,2) \) to get another point \( (0 - 1,2 + 5)=(-1,7) \).

Step4: Draw the line

Draw a straight line passing through the points we have plotted (e.g., \( (0,2) \) and \( (1,-3) \) or \( (0,2) \) and \( (-1,7) \)).

Answer:

To graph \( y=-5x + 2 \):

1. Plot the y - intercept at \( (0,2) \).
2. Use the slope \( - 5 \) to find another point (e.g., from \( (0,2) \), move 1 unit right and 5 units down to get \( (1,-3) \)).
3. Draw a straight line through the plotted points.