Question

If the Y-intercept is (0, 5)

And the other points graphed are: (3, 3) and (6, 1)

What is the slope?

What is the equation of the line in slope-intercept form?

Answer 1

To find the slope of the line given two points and the y-intercept, we can use the formula for slope \( m \):

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

We have the following points:
- Y-intercept: \( (0, 5) \)
- Another point: \( (3, 3) \)

Using these two points, we can assign:
- \( (x_1, y_1) = (0, 5) \)
- \( (x_2, y_2) = (3, 3) \)

Now, substituting in the values into the slope formula:

\[
m = \frac{3 - 5}{3 - 0} = \frac{-2}{3}
\]

So, the slope \( m \) is \( -\frac{2}{3} \).

Now, we can write the equation of the line in slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

From the information given:
- Slope \( m = -\frac{2}{3} \)
- Y-intercept \( b = 5 \)

Substituting these values into the slope-intercept form, we get:

\[
y = -\frac{2}{3}x + 5
\]

Therefore, the slope of the line is \( -\frac{2}{3} \) and the equation of the line in slope-intercept form is:

\[
y = -\frac{2}{3}x + 5
\]