Question

Slope equation

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

What is the slope of this line?

(Line goes from (0, 1) to (3, 7))

What is the equation of this line?

Answer 1

To find the slope (m) of the line that goes from the point (0, 1) to the point (3, 7), we can use the slope formula:

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

Here, we can assign:
- \( (x_1, y_1) = (0, 1) \)
- \( (x_2, y_2) = (3, 7) \)

Now, substituting the values into the formula:

\[
m = \frac{7 - 1}{3 - 0} = \frac{6}{3} = 2
\]

So, the slope of the line is \( m = 2 \).

Next, to find the equation of the line, we can use the point-slope form of the equation of a line:

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

Using the point \( (0, 1) \) and the slope \( m = 2 \):

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

Simplifying this gives:

\[
y - 1 = 2x
\]
\[
y = 2x + 1
\]

Therefore, the equation of the line is:

\[
y = 2x + 1
\]