Question

What is the equation of the line that passes through the points (-9, -3) and (9, 3)?

1. y=−31x+1
2. y=31x+1
3. y=3x+1
4. y=−31x

Answer 1

The equation of the line that passes through the points (-9, -3) and (9, 3) is y = 1/3x, which is obtained by calculating the slope and then using the point-slope form.

Step-by-step explanation:

The equation of the line that passes through two points, (-9, -3) and (9, 3), can be found using the slope formula and the point-slope form of a line. The slope (m) is the change in y over the change in x, so:

m = (y2 - y1) / (x2 - x1) = (3 - (-3)) / (9 - (-9)) = 6 / 18 = 1/3

After finding the slope, we use one of the points and the slope to write the equation in point-slope form, which is y - y1 = m(x - x1). Substituting the values gives:

y - (-3) = 1/3(x - (-9))

Next, simplify and rewrite in slope-intercept form:

y + 3 = 1/3(x + 9)

Multiply through by 3 to get rid of the fraction:

3y + 9 = x + 9

After simplifying, we get:

y = 1/3x + 0

Thus, the correct equation of the line is:

y = 1/3x