Question

7 consider these graphs of linear equations. decide which line has a positive slope, and which has a negative slope. then calculate each lines exact slope.
line m has a \boxed{} slope. the slope of m is \boxed{}.
line l has a \boxed{} slope. the slope of l is \boxed{}

Explanation:

for Line m:

Step1: Identify two points on line m

We can use the points \((5, 20)\) and \((8, -40)\). Let \((x_1, y_1)=(5, 20)\) and \((x_2, y_2)=(8, -40)\).

Step2: Use the slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Substitute the values into the formula:
\(m=\frac{-40 - 20}{8 - 5}=\frac{-60}{3}=- 20\)
Since the slope is negative, line m has a negative slope.

for Line l:

Step1: Identify two points on line l

We can use the points \((8, 80)\) and \((0, -80)\) (from the y - intercept). Let \((x_1, y_1)=(0, -80)\) and \((x_2, y_2)=(8, 80)\).

Step2: Use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\)

Substitute the values into the formula:
\(m=\frac{80-(-80)}{8 - 0}=\frac{160}{8} = 20\)
Since the slope is positive, line l has a positive slope.

Answer:

• line m has a negative slope. The slope of m is \(-20\).
• line l has a positive slope. The slope of l is \(20\).