Question

Slope equation

m = rise/run = y2-y1/x2 - x1

What is the slope of this line?

(Line goes from (0, -1) to (2, 0))

What is the equation of this line?

Answer 1

To find the slope of the line that goes from the point (0, -1) to the point (2, 0), we can use the slope formula:

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

Assigning the points:
- \( (x_1, y_1) = (0, -1) \)
- \( (x_2, y_2) = (2, 0) \)

Now plug in the values:

\[
m = \frac{0 - (-1)}{2 - 0} = \frac{1}{2}
\]

So, the slope \( m \) is \( \frac{1}{2} \).

### Equation of the Line

To find the equation of the line, we can use the point-slope form of the equation of a line, which is:

\[
y - y_1 = m(x - x_1)
\]

We can use one of the points, say (0, -1), and the slope \( m = \frac{1}{2} \):

\[
y - (-1) = \frac{1}{2}(x - 0)
\]

This simplifies to:

\[
y + 1 = \frac{1}{2}x
\]

To put it in slope-intercept form \( y = mx + b \), we can subtract 1 from both sides:

\[
y = \frac{1}{2}x - 1
\]

Thus, the equation of the line is:

\[
y = \frac{1}{2}x - 1
\]