What is the equation of this line?

Responses

y = 3x
y = 3 x

y=−13x
y = − 1 3 x

y=13x
y = 1 3 x

y=−3x
y = − 3 x
Graph of a line passing through the origin and the point begin ordered pair 1 comma 3 end ordered pair.

1 answer

To find the equation of the line that passes through the origin (0,0) and the point (1,3), we can use the slope-intercept form of the equation of a line:

\[ y = mx + b \]

where \( m \) is the slope and \( b \) is the y-intercept. Since the line passes through the origin, the y-intercept \( b \) is 0.

Next, we need to calculate the slope \( m \). The slope is defined as the change in \( y \) divided by the change in \( x \):

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

Using the points (0,0) and (1,3):

\[ m = \frac{3 - 0}{1 - 0} = \frac{3}{1} = 3 \]

Now we can write the equation of the line:

\[ y = 3x \]

So, the correct equation of the line is:

y = 3x