Question

A line passes through the points (4,1) and (8,4) write the equation of the line in the form y = mx+b
y = ______

Answer 1

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

The formula for the slope \( m \) 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 \((4, 1)\) and \((8, 4)\):

- \((x_1, y_1) = (4, 1)\)
- \((x_2, y_2) = (8, 4)\)

Now substitute the values into the slope formula:

\[
m = \frac{4 - 1}{8 - 4} = \frac{3}{4}
\]

Now that we have the slope \( m = \frac{3}{4} \), we can use one of the points to find the y-intercept \( b \). We'll use the point \((4, 1)\).

The equation of the line can be written as:

\[
y = mx + b
\]

Substituting \( m \) and the coordinates of the point into the equation:

\[
1 = \frac{3}{4} \cdot 4 + b
\]

Calculating:

\[
1 = 3 + b
\]

To solve for \( b \):

\[
b = 1 - 3 = -2
\]

Now, we can write the equation of the line:

\[
y = \frac{3}{4}x - 2
\]

So, the equation of the line is:

\[
y = \frac{3}{4}x - 2
\]