Question

What is the of the line in slope- intercept from. (0,-4) (1,-1)

Answer 1

To find the equation of the line in slope-intercept form (y = mx + b) using the points (0, -4) and (1, -1), we first need to determine the slope (m) and then the y-intercept (b).

1. **Calculate the slope (m)**:
The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Plugging in the points \((0, -4)\) and \((1, -1)\):

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

2. **Determine the y-intercept (b)**:
Since one of the given points is (0, -4), we can see that when \(x = 0\), \(y = -4\). Thus, the y-intercept \(b\) is \(-4\).

3. **Write the equation in slope-intercept form**:
Now that we have the slope \(m = 3\) and the y-intercept \(b = -4\), we can write the equation of the line:

\[
y = 3x - 4
\]

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

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