Question

What is (0, -2), (1, 3) graphed in slope intercept form

Answer 1

To find the slope-intercept form of the line that passes through the points (0, -2) and (1, 3), we can follow these steps:

1. **Identify the coordinates of the points**:
- Point 1 (x₁, y₁) = (0, -2)
- Point 2 (x₂, y₂) = (1, 3)

2. **Calculate the slope (m)** of the line using the formula:
\[
m = \frac{y₂ - y₁}{x₂ - x₁}
\]
Substituting the coordinates:
\[
m = \frac{3 - (-2)}{1 - 0} = \frac{3 + 2}{1} = \frac{5}{1} = 5
\]

3. **Use the slope and one of the points to find the y-intercept (b)**. The slope-intercept form of a line is given by the equation:
\[
y = mx + b
\]
We can use the y-intercept point (0, -2) for this:
\[
-2 = 5(0) + b
\]
Simplifying gives:
\[
-2 = b
\]

4. **Write the equation in slope-intercept form**:
Now we can substitute the values of m and b into the slope-intercept form:
\[
y = 5x - 2
\]

So, the equation of the line in slope-intercept form that passes through the points (0, -2) and (1, 3) is:
\[
y = 5x - 2
\]