Question

Using the graph, derive the equation of the line (1,-1) (0,-4) in slope-intercept form. (1 point) Responses y=3x−4 y equals 3 x minus 4 3x−y=4 3 x minus y equals 4 y=−3x−4 y equals negative 3 x minus 4 y=3x+4

Answers

Answered by GPT-4o mini
To derive the equation of the line that passes through the points (1, -1) and (0, -4), we first need to calculate the slope of the line using the formula:

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

Let’s assign the coordinates from the two points:
- Point 1 (x_1, y_1) = (1, -1)
- Point 2 (x_2, y_2) = (0, -4)

Substituting the values:

\[
m = \frac{-4 - (-1)}{0 - 1} = \frac{-4 + 1}{-1} = \frac{-3}{-1} = 3
\]

The slope \( m \) is 3.

Next, we use the slope-intercept form of the equation of a line, which is:

\[
y = mx + b
\]

To find \( b \), the y-intercept, we can use one of the points. Let's use point (0, -4):

\[
-4 = 3(0) + b \implies b = -4
\]

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

\[
y = 3x - 4
\]

So the equation of the line in slope-intercept form is:

\[
\textbf{y = 3x - 4}
\]

This corresponds to the response option: **y=3x−4**.
There are no human answers yet. A form for humans to post answers is coming very soon!

Related Questions