Question

graph this line using the slope and y-intercept: y = 4x - 7 click to select points on the graph. save answer

Explanation:

Step1: Identify y-intercept

The equation is \( y = 4x - 7 \), in slope - intercept form \( y=mx + b \) where \( b \) is the y - intercept. So, when \( x = 0 \), \( y=-7 \). So the y - intercept point is \( (0,-7) \).

Step2: Use slope to find another point

The slope \( m = 4=\frac{4}{1} \). From the y - intercept \( (0,-7) \), we move up 4 units (since the numerator of the slope is 4) and right 1 unit (since the denominator of the slope is 1). So the new point is \( (0 + 1,-7+4)=(1,-3) \). We can also move down 4 units and left 1 unit from the y - intercept: \( (0 - 1,-7-4)=(-1,-11) \). To graph the line, we plot the y - intercept \( (0,-7) \) and then use the slope to find another point (like \( (1,-3) \)) and draw a straight line through these points.

Answer:

To graph \( y = 4x-7 \):

1. Plot the y - intercept: The point is \( (0, - 7) \) (where the line crosses the y - axis).
2. Use the slope \( m = 4=\frac{4}{1} \): From \( (0,-7) \), move 1 unit to the right and 4 units up to get the point \( (1,-3) \) (or 1 unit left and 4 units down to get \( (-1,-11) \)).
3. Draw a straight line through the plotted points (e.g., \( (0,-7) \) and \( (1,-3) \)).