Question

1. graph $y = -4x + 3$

Explanation:

Step1: Identify the form of the equation

The equation \( y = -4x + 3 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m=-4 \) and \( b = 3 \).

Step2: Plot the y - intercept

The y - intercept \( b = 3 \) means the line crosses the y - axis at the point \( (0,3) \). So we plot the point \( (0,3) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m=-4=\frac{-4}{1} \). The slope is the ratio of the change in \( y \) (rise) to the change in \( x \) (run). Starting from the point \( (0,3) \), since the slope is \( \frac{-4}{1} \), we move down 4 units (because the numerator is - 4, which represents a decrease in \( y \)) and then 1 unit to the right (because the denominator is 1, which represents an increase in \( x \)). This gives us the point \( (0 + 1,3-4)=(1,-1) \). We can also move up 4 units and left 1 unit from \( (0,3) \) to get another point \( (0 - 1,3 + 4)=(-1,7) \).

Step4: Draw the line

After plotting at least two points (e.g., \( (0,3) \) and \( (1,-1) \) or \( (0,3) \) and \( (-1,7) \)), we draw a straight line passing through these points.

To graph the line \( y=-4x + 3 \):

1. Plot the y - intercept at \( (0,3) \).
2. Use the slope \( m = - 4\) to find additional points (e.g., from \( (0,3) \), moving 1 unit right and 4 units down gives \( (1,-1) \), or 1 unit left and 4 units up gives \( (-1,7) \)).
3. Draw a straight line through the plotted points.

(If we were to describe the graph in terms of its key features: It is a straight line with a negative slope (sloping downwards from left to right), crossing the y - axis at \( (0,3) \), and for every 1 unit increase in \( x \), \( y \) decreases by 4 units.)

Answer:

Step1: Identify the form of the equation

The equation \( y = -4x + 3 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m=-4 \) and \( b = 3 \).

Step2: Plot the y - intercept

The y - intercept \( b = 3 \) means the line crosses the y - axis at the point \( (0,3) \). So we plot the point \( (0,3) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m=-4=\frac{-4}{1} \). The slope is the ratio of the change in \( y \) (rise) to the change in \( x \) (run). Starting from the point \( (0,3) \), since the slope is \( \frac{-4}{1} \), we move down 4 units (because the numerator is - 4, which represents a decrease in \( y \)) and then 1 unit to the right (because the denominator is 1, which represents an increase in \( x \)). This gives us the point \( (0 + 1,3-4)=(1,-1) \). We can also move up 4 units and left 1 unit from \( (0,3) \) to get another point \( (0 - 1,3 + 4)=(-1,7) \).

Step4: Draw the line

After plotting at least two points (e.g., \( (0,3) \) and \( (1,-1) \) or \( (0,3) \) and \( (-1,7) \)), we draw a straight line passing through these points.

To graph the line \( y=-4x + 3 \):

1. Plot the y - intercept at \( (0,3) \).
2. Use the slope \( m = - 4\) to find additional points (e.g., from \( (0,3) \), moving 1 unit right and 4 units down gives \( (1,-1) \), or 1 unit left and 4 units up gives \( (-1,7) \)).
3. Draw a straight line through the plotted points.

(If we were to describe the graph in terms of its key features: It is a straight line with a negative slope (sloping downwards from left to right), crossing the y - axis at \( (0,3) \), and for every 1 unit increase in \( x \), \( y \) decreases by 4 units.)