Question

What is the of the line in slope- intercept from. (0,4) (1,8)

Answer 1

To find the equation of a line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b) using the two given points: (0, 4) and (1, 8).

1. **Calculate the slope (m)**:
The formula for slope is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (0, 4) as \((x_1, y_1)\) and (1, 8) as \((x_2, y_2)\):
\[
m = \frac{8 - 4}{1 - 0} = \frac{4}{1} = 4
\]

2. **Determine the y-intercept (b)**:
Since one of the points (0, 4) has an x-coordinate of 0, the y-coordinate at this point is the y-intercept. Therefore, \(b = 4\).

3. **Write the equation**:
Now that we have the slope \(m = 4\) and the y-intercept \(b = 4\), we can write the equation of the line:
\[
y = 4x + 4
\]

Thus, the equation of the line in slope-intercept form is \(y = 4x + 4\).