What is the y-intercept of this line

Question

(Line goes from (0, -3) (3, 0))

What is the equation of the libe

GPT-4o mini · Answer

To find the equation of the line that passes through the points (0, -3) and (3, 0), we can use the slope-intercept form of the equation of a line, which is given by:

$y = m x + b$

where $m$ is the slope and $b$ is the y-intercept.

Step 1: Calculate 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 (0, -3) $(x_{1}, y_{1})$ and (3, 0) $(x_{2}, y_{2})$ :

$m = \frac{0 - (- 3)}{3 - 0} = \frac{3}{3} = 1$

Step 2: Determine the y-intercept (b)

The y-intercept $b$ is the y-coordinate of the point where the line crosses the y-axis, which is the $y$ -coordinate when $x = 0$ . From the point (0, -3), we can see that:

$b = - 3$

Step 3: Write the equation of the line

Now that we have the slope and y-intercept, we can write the equation of the line:

$y = 1 x - 3 or simply y = x - 3$

Summary

The y-intercept of the line is $- 3$ .
The equation of the line is $y = x - 3$ .