Question

Given that the points (0,3) and (2,5) lie on a line. What is the equation for that line in the slope-intercept (
) form?

Answer 1

To find the equation of the line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b).

1. **Calculate the slope (m)**:

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \((0, 3)\) and \((2, 5)\):
- \( (x_1, y_1) = (0, 3) \)
- \( (x_2, y_2) = (2, 5) \)

Now plug in the values:
\[
m = \frac{5 - 3}{2 - 0} = \frac{2}{2} = 1
\]

2. **Find the y-intercept (b)**:

The y-intercept \( b \) occurs when \( x = 0 \). From the point \((0,3)\), we have:
\[
b = 3
\]

3. **Write the equation**:

Now that we have the slope \( m = 1 \) and the y-intercept \( b = 3 \), we can write the equation of the line in slope-intercept form:
\[
y = mx + b
\]

Substituting in the values, we get:
\[
y = 1x + 3
\]

This simplifies to:
\[
y = x + 3
\]

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