graph the following features: - slope = 4 - y-intercept = -1

Explanation:

Step1: Recall Slope-Intercept Form

The slope - intercept form of a linear equation is (y = mx + b), where (m) is the slope and (b) is the y - intercept. Given (m = 4) and (b=-1), the equation of the line is (y=4x - 1).

Step2: Plot the Y - intercept

The y - intercept is ((0,b)=(0, - 1)). So we first mark the point ((0,-1)) on the y - axis.

Step3: Use the Slope to Find Another Point

The slope (m = 4=\frac{4}{1}), which means for a run of (1) (change in (x)), the rise is (4) (change in (y)). Starting from the point ((0,-1)), if we move (1) unit to the right (increase (x) by (1)) to (x = 1), we move (4) units up (increase (y) by (4)) from (y=-1) to (y=-1 + 4=3). So we get the point ((1,3)).

Step4: Draw the Line

Draw a straight line passing through the points ((0,-1)) and ((1,3)) (and extending in both directions). The existing line in the graph has a negative slope, so we need to draw a new line with a positive slope of (4) and y - intercept (-1).

Answer:

To graph the line with slope (4) and y - intercept (-1):

1. Plot the point ((0,-1)) (the y - intercept).
2. From ((0,-1)), move (1) unit right and (4) units up to plot the point ((1,3)).
3. Draw a straight line through ((0,-1)) and ((1,3)) (extending in both directions). The final graph should be a line with a steep positive slope passing through ((0, - 1)) and ((1,3)).