Question

Which can be the first step in finding the equation of the line that passes through the points (5, negative 4) and (negative 1, 8) in slope-intercept form?
Calculate StartFraction 8 minus (negative 4) Over negative 1 minus 5 EndFraction = StartFraction 12 Over negative 6 EndFraction = negative 2..
Calculate StartFraction negative 1 minus 5 Over 8 minus (negative 4) EndFraction = StartFraction negative 6 Over 12 EndFraction = negative one-half..
Find that the point at which the line intersects with the line y = 0 is (3, 0).
Find that the point at which the line intersects with the line x = y is (2, 2).

Answer 1

To find the equation of the line that passes through the points (5, -4) and (-1, 8), the first step is to calculate the slope of the line using the two given points. The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

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

Let’s assign the points:
- Point 1: \( (x_1, y_1) = (5, -4) \)
- Point 2: \( (x_2, y_2) = (-1, 8) \)

Substituting the values into the formula, we have:

\[
m = \frac{8 - (-4)}{-1 - 5}
\]

Calculating this gives:

\[
m = \frac{8 + 4}{-1 - 5} = \frac{12}{-6} = -2
\]

So the slope \( m = -2 \).

Now, the next step would be to use the point-slope form of the linear equation, which is given by:

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

You can use either of the points, but let’s use \( (5, -4) \):

\[
y - (-4) = -2(x - 5)
\]

Simplifying this, we get:

\[
y + 4 = -2(x - 5)
\]
\[
y + 4 = -2x + 10
\]
\[
y = -2x + 10 - 4
\]
\[
y = -2x + 6
\]

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

\[
y = -2x + 6
\]

From here, you could check specific points regarding their intersections with other lines, but calculating the slope was the essential first step in this problem.