Question

Use point-slope form, y - y1 = m(x - x1), to find the linear equation of a line that passes through the points
(2, -1) and (10, 7).

y =
x
+

Answer 1

To find the linear equation of the line that passes through the points (2, -1) and (10, 7), we will first need to calculate the slope (m) of the line using the formula:

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

Where \((x_1, y_1) = (2, -1)\) and \((x_2, y_2) = (10, 7)\).

Substituting the coordinates into the slope formula:

\[
m = \frac{7 - (-1)}{10 - 2} = \frac{7 + 1}{10 - 2} = \frac{8}{8} = 1
\]

Now that we have the slope \(m = 1\), we can use the point-slope form of the equation of a line, which is given by:

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

We can use either point, but let's use the point (2, -1):

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

Simplifying this, we have:

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

\[
y + 1 = x - 2
\]

Now, we can isolate \(y\):

\[
y = x - 2 - 1
\]

\[
y = x - 3
\]

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

\[
y = x - 3
\]

To represent this in the required format \(y = mx + b\), we have:

\[
y = 1 \cdot x + (-3)
\]

So, the final answer is:

\[
y = x - 3
\]

In the format you requested, the answer can be stated as:
- \(m = 1\)
- \(b = -3\)

So, indeed,
\[
y = x + (-3)
\]