Question

1

6. A triangle has vertices A(1, 1), B(2, 4), and C(4, 2). Line fis parallel to side AB and
contains point C. Write an equation for line f.
0
3
C
2
B
b
a
4
5
6
Part 1: Find the slope of AB. Show your work. (1 point)
Part II: Use the slope from Part I and point C to write an equation for line fin
slope-intercept form. Show your work. (2 points)

Answer 1

Sure, I'd be happy to help!

Part 1: Find the slope of AB

To find the slope of AB, we need to find the rise (change in y-values) and run (change in x-values) between the two points.

First, let's find the rise and run of AB:

Rise = y2 - y1 = 4 - 1 = 3

Run = x2 - x1 = 2 - 1 = 1

Now, we can calculate the slope of AB using the formula:

Slope = Rise / Run = 3 / 1 = 3

So, the slope of AB is 3.

Part II: Write an equation for line f in slope-intercept form

Now that we have the slope of AB, we can write an equation for line f in slope-intercept form.

The equation of a line in slope-intercept form is:

y = mx + b

where m is the slope, and b is the y-intercept.

In this case, the slope of AB is 3, and the y-intercept is 1 (since the line passes through point C, which has a y-value of 1).

So, the equation of line f in slope-intercept form is:

y = 3x + 1

BOLD the answer:

y = 3x + 1

Explanation: