Question

find the slope of each line defined below and compare their values.
equation of line a:
y - 10 = -5(x + 1)
select values from line b:

x	y
-4	3
-2	0
0	-3
2	-6

answer attempt 1 out of 2
the slope of line a is and the slope of line b is . therefore the slope of line a is the slope of line b.

Explanation:

Step1: Find slope of Line A

The equation of Line A is in point - slope form \(y - y_1=m(x - x_1)\), where \(m\) is the slope. For the equation \(y - 10=-5(x + 1)\), comparing with \(y - y_1=m(x - x_1)\) (here \(x_1=- 1,y_1 = 10\)), the slope \(m\) of Line A is \(-5\).

Step2: Find slope of Line B

We use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points from the table of Line B. Let's take \((x_1,y_1)=(-4,3)\) and \((x_2,y_2)=(-2,0)\). Then \(m=\frac{0 - 3}{-2-(-4)}=\frac{-3}{2}=-\frac{3}{2}\). We can check with another pair of points, say \((-2,0)\) and \((0,-3)\). \(m=\frac{-3 - 0}{0-(-2)}=\frac{-3}{2}=-\frac{3}{2}\), so the slope of Line B is \(-\frac{3}{2}\).

Step3: Compare the slopes

We have slope of Line A \(m_A=-5\) and slope of Line B \(m_B =-\frac{3}{2}\). To compare \(-5\) and \(-\frac{3}{2}\), we know that \(-5=-\frac{10}{2}\), and since \(-\frac{10}{2}<-\frac{3}{2}\), the slope of Line A is less than the slope of Line B.

Answer:

The slope of Line A is \(-5\) and the slope of Line B is \(-\frac{3}{2}\). Therefore the slope of Line A is less than the slope of Line B.