the equation y=mx

Question

for a line through the origin. Simplify the numerical coefficient, if needed
first point (3,3) second point (8,8)

Answer 1

To find the equation of the line that goes through the points (3, 3) and (8, 8), we first need to determine the slope \( m \) of the line.

The slope \( m \) is calculated using the formula:

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

Using the points (3, 3) (where \( (x_1, y_1) = (3, 3) \)) and (8, 8) (where \( (x_2, y_2) = (8, 8) \)):

\[ m = \frac{8 - 3}{8 - 3} = \frac{5}{5} = 1 \]

Now that we have the slope \( m = 1 \), we can write the equation of the line through the origin:

\[ y = mx \quad \Rightarrow \quad y = 1x \]

For simplicity, we can write:

\[ y = x \]

So the equation of the line that passes through the points (3, 3) and (8, 8) is \( y = x \).