Question

graph the line with slope $-\dfrac{3}{4}$ and $y$-intercept 2.

Explanation:

Step1: Identify the y-intercept

The y-intercept is 2, so we start by plotting the point (0, 2) on the y-axis.

Step2: Use the slope to find another point

The slope is $-\frac{3}{4}$, which means for every 4 units we move to the right (positive x-direction), we move down 3 units (negative y-direction). From (0, 2), moving 4 units right to x = 4 and 3 units down gives us the point (4, 2 - 3) = (4, -1). Alternatively, we can move 4 units left (negative x-direction) and 3 units up (positive y-direction) from (0, 2) to get (-4, 2 + 3) = (-4, 5).

Step3: Draw the line

Connect the points (0, 2) and (4, -1) (or other points found using the slope) with a straight line to graph the line.

Answer:

To graph the line:

1. Plot the y - intercept point (0, 2) on the y - axis.
2. Use the slope $-\frac{3}{4}$: from (0, 2), move 4 units right and 3 units down to get (4, - 1), or 4 units left and 3 units up to get (-4, 5).
3. Draw a straight line through the plotted points. The line should pass through (0, 2), (4, -1), (-4, 5), etc. (The actual graph is a straight line with the given slope and y - intercept as described above.)