Question

Slope Equation rise
m =
run
=
У2 - У1
Х2 -X1
What is the slope of this line?
10-
• (3, 7)
6
(0, 1) °
3'
-10
10
-10-
slope =
type your answer...
What is the equation of this line?

Answer 1

To find the slope (m) of the line passing through the points \( (0, 1) \) and \( (3, 7) \), we can use the slope formula:

\[
m = \frac{Y_2 - Y_1}{X_2 - X_1}
\]

Here, \( (X_1, Y_1) = (0, 1) \) and \( (X_2, Y_2) = (3, 7) \).

1. First, substitute 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, which is:

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

Substituting the slope and one of the points, say \( (0, 1) \):

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

This simplifies to:

\[
y - 1 = 2x
\]

Now, solving for \( y \):

\[
y = 2x + 1
\]

Thus, the equation of the line is \( y = 2x + 1 \).

In summary:
- The slope is \( 2 \).
- The equation of the line is \( y = 2x + 1 \).