Question

for problems 2 - 7, find the slope of the line.

Explanation:

Step1: Recall slope - formula

The slope formula for a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Identify two points on the line (for problem 2)

Let's take two points on the line in problem 2. For example, $(0,0)$ and $(4,4)$. Here $x_1 = 0,y_1 = 0,x_2=4,y_2 = 4$.

Step3: Calculate the slope for problem 2

Substitute the values into the slope - formula: $m=\frac{4 - 0}{4 - 0}=1$.

Step4: Identify two points on the line (for problem 3)

Take two points, say $(- 4,-2)$ and $(4,2)$. Here $x_1=-4,y_1 = - 2,x_2 = 4,y_2=2$.

Step5: Calculate the slope for problem 3

$m=\frac{2-(-2)}{4-(-4)}=\frac{2 + 2}{4 + 4}=\frac{4}{8}=\frac{1}{2}$.

Step6: Identify two points on the line (for problem 4)

Let the points be $(0,0)$ and $(6,3)$. Here $x_1 = 0,y_1 = 0,x_2=6,y_2 = 3$.

Step7: Calculate the slope for problem 4

$m=\frac{3 - 0}{6 - 0}=\frac{1}{2}$.

Step8: Identify two points on the line (for problem 5)

Take points $(0,0)$ and $(2,6)$. Here $x_1 = 0,y_1 = 0,x_2=2,y_2 = 6$.

Step9: Calculate the slope for problem 5

$m=\frac{6 - 0}{2 - 0}=3$.

Answer:

Problem 2: 1
Problem 3: $\frac{1}{2}$
Problem 4: $\frac{1}{2}$
Problem 5: 3