Question

graph a line through (5, 7) and has a slope of $-dfrac{4}{3}$

Explanation:

Step1: Recall the slope formula

The slope \( m = \frac{y_2 - y_1}{x_2 - x_1} \), here \( m = -\frac{4}{3} \), \( (x_1,y_1)=(5,7) \). Let the next point be \( (x_2,y_2) \). So \( -\frac{4}{3}=\frac{y_2 - 7}{x_2 - 5} \)

Step2: Find a new point

We can choose to change \( x \) by 3 (denominator of slope) and \( y \) by - 4 (numerator of slope). So if \( x_2=x_1 + 3=5 + 3 = 8 \), then \( y_2=y_1-4 = 7-4=3 \). So one new point is \( (8,3) \). Or if \( x_2=x_1-3 = 5 - 3=2 \), then \( y_2=y_1 + 4=7 + 4 = 11 \) (but 11 may be out of graph, so better use \( (8,3) \) or \( (2,11) \) or other combinations. Another way: from \( (5,7) \), moving 3 units left (since slope is negative, change in x and y: rise over run, run is 3, rise is - 4) so \( x = 5-3 = 2 \), \( y=7 + 4 = 11 \); or 3 units right, \( x = 5 + 3=8 \), \( y=7-4 = 3 \).

Step3: Plot the points

Plot the point \( (5,7) \) first. Then plot the new point we found, say \( (8,3) \) or \( (2,11) \), then draw a line through them.

Answer:

To graph the line:

1. Plot the point \((5, 7)\) on the coordinate plane.
2. Use the slope \(m = -\frac{4}{3}\) (which means for every 3 units you move to the right along the x - axis, you move 4 units down along the y - axis, or for every 3 units you move to the left, you move 4 units up).

• For example, from \((5, 7)\), move 3 units to the right (to \(x=5 + 3=8\)) and 4 units down (to \(y = 7-4 = 3\)) to get the point \((8, 3)\). Or move 3 units to the left (to \(x = 5-3=2\)) and 4 units up (to \(y=7 + 4 = 11\)) to get the point \((2, 11)\).

1. Draw a straight line through the points \((5, 7)\) and the new point (e.g., \((8, 3)\) or \((2, 11)\)) to represent the line with slope \(-\frac{4}{3}\) passing through \((5, 7)\).