Question

graphing a linear equation of the form
$y = mx + b$
graph each linear equation on the grid provided. be sure to label the
units on the x- and y-axes.
1 $y = -2x + 1$

2 $y = 40x - 20$

Explanation:

Step1: Analyze \( y = -2x + 1 \)

The equation is in slope - intercept form \( y=mx + b \), where \( m=-2 \) (slope) and \( b = 1 \) (y - intercept).

• Plot the y - intercept: The y - intercept is \( (0,1) \). So we mark the point \( (0,1) \) on the coordinate grid.
• Use the slope to find another point: The slope \( m=-2=\frac{-2}{1} \). From the point \( (0,1) \), we move down 2 units (because the numerator of the slope is - 2) and then 1 unit to the right (because the denominator of the slope is 1). This gives us the point \( (1,1 - 2)=(1,-1) \). We can also move up 2 units and 1 unit to the left (since slope is also \( \frac{2}{-1} \)) from \( (0,1) \) to get \( (-1,3) \).
• Draw a line: Connect the points \( (0,1) \), \( (1,-1) \), \( (-1,3) \) (or other points found using the slope) with a straight line. Label the x - axis and y - axis with appropriate units (e.g., each grid square represents 1 unit).

Step2: Analyze \( y = 40x-20 \)

The equation is in slope - intercept form \( y = mx + b \), where \( m = 40 \) (slope) and \( b=-20 \) (y - intercept).

• Plot the y - intercept: The y - intercept is \( (0,-20) \). Mark the point \( (0,-20) \) on the coordinate grid.
• Use the slope to find another point: The slope \( m = 40=\frac{40}{1} \). From the point \( (0,-20) \), we move up 40 units and 1 unit to the right. This gives us the point \( (1,-20 + 40)=(1,20) \). We can also move down 40 units and 1 unit to the left from \( (0,-20) \) to get \( (-1,-60) \). But since the slope is very large, the line will be very steep.
• Draw a line: Connect the points \( (0,-20) \) and \( (1,20) \) (or other points found using the slope) with a straight line. Label the x - axis and y - axis with appropriate units. For this equation, since the slope is 40, the scale of the axes may need to be adjusted (e.g., the y - axis can have a larger scale or we can use a different unit representation to show the line clearly).

Answer:

For \( y=-2x + 1 \): Plot \( (0,1) \), use slope \( - 2 \) to find other points (e.g., \( (1,-1) \)), draw a line. For \( y = 40x-20 \): Plot \( (0,-20) \), use slope \( 40 \) to find other points (e.g., \( (1,20) \)), draw a line. (The actual graphing is done on the provided grids with labeled axes.)