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

Question

(1 point)
Responses

equation
Image with alt text: equation

equation
Image with alt text: equation

equation
Image with alt text: equation

equation

Answer 1

The equation of a line passing through two points (x1, y1) and (x2, y2) is found using the slope-intercept form:

y - y1 = m(x - x1)

Where m is the slope of the line.

Given the points (6, -3) and (-4, -9), we can find the slope:

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

m = (-9 - (-3)) / (-4 - 6)

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

m = -6 / -10

m = 3/5

Now that we have the slope, we can use the point-slope form with one of the points:

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

Simplified:

y + 3 = (3/5)(x - 6) [equation 1]

Multiplying through by 5 to eliminate the fraction:

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

5y + 15 = 3x - 18

Rearranging:

3x - 5y = 33 [equation 2]

So, the equation of the line passing through the points (6, -3) and (-4, -9) is either equation 1 or equation 2.