Let's go through the steps to determine the required values.
Step 1: Calculate the slope and y-intercept of line AB
Given points:
- Point A: (8, 0)
- Point B: (3, 7)
First, calculate the slope (m) of line AB.
[tex]\[
\text{slope}_{AB} = \frac{y_B - y_A}{x_B - x_A} = \frac{7 - 0}{3 - 8} = \frac{7}{-5} = -1.4
\][/tex]
Next, use the slope to find the y-intercept (c) of line AB using point A (8, 0).
[tex]\[
y = mx + c \implies 0 = (-1.4) \cdot 8 + c \implies 0 = -11.2 + c \implies c = 11.2
\][/tex]
So, the y-intercept of AB is [tex]\(11.2\)[/tex].
Step 2: Calculate the slope and y-intercept of line CD
Given points:
- Point C: (5, 5)
- Point D: (9, 10)
Calculate the slope (m) of line CD.
[tex]\[
\text{slope}_{CD} = \frac{y_D - y_C}{x_D - x_C} = \frac{10 - 5}{9 - 5} = \frac{5}{4} = 1.25
\][/tex]
Next, use the slope to find the y-intercept (c) of line CD using point C (5, 5).
[tex]\[
y = mx + c \implies 5 = 1.25 \cdot 5 + c \implies 5 = 6.25 + c \implies c = 5 - 6.25 = -1.25
\][/tex]
So, the equation of line CD is:
[tex]\[
y = 1.25x - 1.25
\][/tex]
To summarize the final answers:
- The y-intercept of AB is [tex]\(11.2\)[/tex].
- The equation of line CD is [tex]\(y = 1.25x - 1.25\)[/tex].
