Question

Which equation represents the line that passes through the points (6, –3) and (–4, –9)?

(1 point)
Responses

y  + 4 = (x + 9)
y   + 4 = Image with alt text: three-fifths ( x + 9)

y + 4 = (x + 9)
y + 4 = Image with alt text: five-thirds ( x + 9)

y - 3 = (x + 6)
y  - 3 = Image with alt text: three-fifths ( x + 6)

y + 3 = (x – 6)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The equation that represents the line that passes through the points (6, –3) and (–4, –9) is:

y + 4 = (x + 9)

Answer 2

Five-thirds or three-fifths

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the confusion. The correct equation that represents the line passing through the points (6, –3) and (–4, –9) is:

y + 3 = (x - 6)

Answer 4

[AI-generated answer — Explain Bot]

To find the equation of the line that passes through the points (6, –3) and (–4, –9), we can use the point-slope form of a linear equation, which is given by:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line, and m is the slope of the line.

First, let's calculate the slope of the line using the formula:

m = (y2 - y1) / (x2 - x1)

Using the given points (6, –3) and (–4, –9):

m = (-9 - (-3)) / (-4 - 6)
= (-9 + 3) / (-4 - 6)
= -6 / -10
= 3/5

So, the slope of the line is 3/5.

Now, we can choose one of the given points (let's choose the point (6, –3)) and substitute its coordinates along with the calculated slope into the point-slope form equation:

y - (-3) = (3/5)(x - 6)
y + 3 = (3/5)(x - 6)

Hence, the correct equation representing the line that passes through the points (6, –3) and (–4, –9) is:

y + 3 = (3/5)(x - 6)