Question

7 a line passes through points a and b shown on the graph. a. what is the difference in the y -values between the two points? b. what is the difference in the x -values between the two points? c. what is the slope of the line passing through a and b?

Explanation:

Step1: Identify y - values of points

Let's assume the y - value of point A is $y_A=-2$ and the y - value of point B is $y_B = 3$.

Step2: Calculate difference in y - values

$\Delta y=y_B - y_A=3-(-2)=5$

Step3: Identify x - values of points

Let's assume the x - value of point A is $x_A = 1$ and the x - value of point B is $x_B=0$.

Step4: Calculate difference in x - values

$\Delta x=x_B - x_A=0 - 1=-1$

Step5: Calculate the slope

The slope $m$ of a line passing through two points is given by $m=\frac{\Delta y}{\Delta x}$. Substituting $\Delta y = 5$ and $\Delta x=-1$, we get $m=\frac{5}{-1}=-5$

Answer:

a. 5
b. -1
c. -5