Question

Using the graph, derive the equation of the line in slope-intercept form (0,3) (3,2)

Answer 1

To derive the equation of the line in slope-intercept form (y = mx + b) using the points (0, 3) and (3, 2), we first need to determine the slope (m) of the line.

The slope (m) is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
where (x₁, y₁) = (0, 3) and (x₂, y₂) = (3, 2).

Substituting the values into the formula:
\[
m = \frac{2 - 3}{3 - 0} = \frac{-1}{3}
\]

Now that we have the slope, we can use one of the points to find the y-intercept (b). The point (0, 3) indicates that when x = 0, y = 3, which means the y-intercept (b) is 3.

Now we have:
- Slope (m) = -\(\frac{1}{3}\)
- Y-intercept (b) = 3

We can now write the equation of the line in slope-intercept form:
\[
y = -\frac{1}{3}x + 3
\]

Therefore, the equation of the line in slope-intercept form is:
\[
y = -\frac{1}{3}x + 3
\]