Question

Find the slope-intercept form of the trend line using these points:
(4, 16)
(6, 14)

16 - 14
6 - 4

=
2/2 simplify if not already if it is then leave it


y = mx + b

? = 2/2(?) + b

? = ? + b

subtract both sides then

you get ? = b

Answer 1

To find the slope-intercept form of the trend line using the given points (4, 16) and (6, 14), let's go through the steps systematically.

1. **Calculate the slope (m)**:
The formula for the slope \( m \) is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (4, 16) \((x_1, y_1)\) and (6, 14) \((x_2, y_2)\):
\[
m = \frac{14 - 16}{6 - 4} = \frac{-2}{2} = -1
\]

2. **Use the slope-intercept form (y = mx + b)**:
We now have \( m = -1 \). Therefore, the equation becomes:
\[
y = -1x + b
\]
or
\[
y = -x + b
\]

3. **Find the y-intercept (b)**:
We can use one of the points to find \( b \). Let's use the point (4, 16):
\[
16 = -1(4) + b
\]
Simplifying this:
\[
16 = -4 + b
\]
Adding 4 to both sides:
\[
b = 20
\]

4. **Write the final equation**:
Now that we have \( m \) and \( b \), the equation in slope-intercept form is:
\[
y = -x + 20
\]

So the trend line in slope-intercept form is:
\[
y = -x + 20
\]