Question

What equation explains this line?
(-2,4) (1,13)

y-4=3(x-2)
y-2=3(x-4)
y-4=3(x+2)
y-1=3(x-13)

Answer 1

To find the equation of the line passing through the points \((-2, 4)\) and \((1, 13)\), we first calculate the slope \(m\) of the line using the formula:

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

Here, \((x_1, y_1) = (-2, 4)\) and \((x_2, y_2) = (1, 13)\):

\[
m = \frac{13 - 4}{1 - (-2)} = \frac{9}{3} = 3
\]

Now we have the slope \(m = 3\).

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

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

We can use either of the given points. Using point \((-2, 4)\):

\[
y - 4 = 3(x - (-2))
\]
\[
y - 4 = 3(x + 2)
\]

So, the equation in point-slope form is:

\[
y - 4 = 3(x + 2)
\]

Now let's compare this to the options you provided:

1. \(y - 4 = 3(x - 2)\)
2. \(y - 2 = 3(x - 4)\)
3. \(y - 4 = 3(x + 2)\)
4. \(y - 1 = 3(x - 13)\)

The correct equation that describes the line passing through the points \((-2, 4)\) and \((1, 13)\) is:

\[
y - 4 = 3(x + 2)
\]

Thus, the answer is option 3.