Question

Which equation describes the line passing through points (-5,-1) and (5,5)?

A) y = (3/5)x + 2
B) y = (5/3)x + 2
C) y = -(5/3)x + 2
D) y = -(3/5)x + 2

Answer 1

The equation of the line passing through the points (-5,-1) and (5,5) is y=(3/5)x+2.

Step-by-step explanation:

To find the equation of the line passing through the points (-5,-1) and (5,5), we need to calculate the slope of the line. The slope formula is given by:

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

Substituting the given coordinates, we have:

1. m = (5 - (-1)) / (5 - (-5))
2. m = 6 / 10
3. m = 3 / 5

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Since the slope is 3/5, the equation of the line passing through the points (-5,-1) and (5,5) is y = (3/5)x + b. To find the value of b, we can substitute the coordinates of one of the points. Let's use (-5,-1):

-1 = (3/5)(-5) + b

1. -1 = -3 + b
2. b = 2

Therefore, the equation of the line is y = (3/5)x + 2, which corresponds to option A.