Question

Derive the equation of the line in slope-intercept form. the numbers are (1,8) and (0,4)

Answer 1

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

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

The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points (1, 8) and (0, 4), we can assign:
- \( (x_1, y_1) = (1, 8) \)
- \( (x_2, y_2) = (0, 4) \)

Substituting these values into the slope formula:

\[
m = \frac{4 - 8}{0 - 1} = \frac{-4}{-1} = 4
\]

So, the slope \( m = 4 \).

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

The y-intercept is the value of \( y \) when \( x = 0 \). From the second point (0, 4), we see that when \( x = 0 \), \( y = 4 \). Therefore, the y-intercept \( b = 4 \).

3. **Write the equation in slope-intercept form**:

Now that we have \( m \) and \( b \), we can write the equation of the line:

\[
y = mx + b
\]

Substituting \( m = 4 \) and \( b = 4 \):

\[
y = 4x + 4
\]

Thus, the equation of the line in slope-intercept form is:

\[
y = 4x + 4
\]