Question

Derive the equation of the line in slope-intercept form.


the first dot 0,4
the second dot 1,8

Answer 1

To derive the equation of a line in slope-intercept form, we use the formula:

\[ y = mx + b \]

where \( m \) is the slope of the line and \( b \) is the y-intercept.

### Step 1: Calculate the Slope (m)

The slope \( m \) can be calculated using the formula:

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

Given the points (0, 4) and (1, 8):

- Point 1: \( (x_1, y_1) = (0, 4) \)
- Point 2: \( (x_2, y_2) = (1, 8) \)

Substituting these values into the slope formula:

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

### Step 2: Find the y-intercept (b)

To find the y-intercept \( b \), we can use one of the points and the slope. We'll use the point \( (0, 4) \). The y-intercept is the \( y \)-coordinate when \( x = 0 \). From the point, we can see:

\[
b = 4
\]

### Step 3: Write the Equation in Slope-Intercept Form

Now we can write the equation of the line using the slope and y-intercept we found:

\[
y = 4x + 4
\]

### Final Result

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

\[
y = 4x + 4
\]