Question

Graphing equations practice. Derive the equation of the line (0,4) (1,8) in slope-intercept form.

Answer 1

To derive the equation of the line given the points \((0, 4)\) and \((1, 8)\), we can follow these steps:

1. **Calculate the slope (m)**:
The slope \(m\) of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Here, \((x_1, y_1) = (0, 4)\) and \((x_2, y_2) = (1, 8)\). Plugging in the values:
\[
m = \frac{8 - 4}{1 - 0} = \frac{4}{1} = 4
\]

2. **Use the point-slope form of the line**:
The point-slope form of the line is given by:
\[
y - y_1 = m(x - x_1)
\]
We'll use one of the points, say \((0, 4)\), and the slope \(m = 4\):
\[
y - 4 = 4(x - 0)
\]

3. **Simplify to slope-intercept form (y = mx + b)**:
Distributing the slope:
\[
y - 4 = 4x
\]
Adding \(4\) to both sides gives:
\[
y = 4x + 4
\]

So, the equation of the line in slope-intercept form is:
\[
y = 4x + 4
\]