Question

this means: example 3 (*fluency practice with pre - requisite) find the slope of a line that passes through each pair of points. a. (-3,4)and (1,7) b. (-2,-5)and (4,-5) step 1: identify and label (x1,y1) and (x2,y2) step 2: use the rate of change (slope) formula example 3 check find the slope of a line that passes through each pair of points. a. (-3.2,-2.4)and (4,1.8) b. (-1,3)and (4,1)

Explanation:

Step1: Identify points for part a of Example 3

Let $(x_1,y_1)=(-3,4)$ and $(x_2,y_2)=(1,7)$.

Step2: Apply slope - formula

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Substitute the values: $m=\frac{7 - 4}{1-(-3)}=\frac{3}{4}$.

Step3: Identify points for part b of Example 3

Let $(x_1,y_1)=(-2,-5)$ and $(x_2,y_2)=(4,-5)$.

Step4: Apply slope - formula

$m=\frac{-5-(-5)}{4 - (-2)}=\frac{-5 + 5}{4+2}=0$.

Step5: Identify points for part a of Example 3 Check

Let $(x_1,y_1)=(-3.2,-2.4)$ and $(x_2,y_2)=(4,1.8)$.

Step6: Apply slope - formula

$m=\frac{1.8-(-2.4)}{4-(-3.2)}=\frac{1.8 + 2.4}{4 + 3.2}=\frac{4.2}{7.2}=\frac{7}{12}$.

Step7: Identify points for part b of Example 3 Check

Let $(x_1,y_1)=(-1,3)$ and $(x_2,y_2)=(4,1)$.

Step8: Apply slope - formula

$m=\frac{1 - 3}{4-(-1)}=\frac{-2}{5}=-\frac{2}{5}$.

Answer:

a. For Example 3: $\frac{3}{4}$; For Example 3 Check: $\frac{7}{12}$
b. For Example 3: $0$; For Example 3 Check: $-\frac{2}{5}$