Question

Write an equation of the line that passes through the pair of points (-5, -2) and (3, -1).

1) y = (1/8)x + (11/8)
2) y = (1/8)x - (11/8)
3) y = -(1/8)x - (11/8)
4) y = (1/8)x + (8/11)

Answer 1

To find the equation of the line through (-5, -2) and (3, -1), the slope is calculated as 1/8 and using the point-slope form, the y-intercept is found to be -11/8. The equation of the line is y = (1/8)x - (11/8).

Step-by-step explanation:

To write an equation of the line that passes through the points (-5, -2) and (3, -1), we first need to find the slope (m) of the line using the formula:

m = (y2 - y1) / (x2 - x1) = (-1 - (-2)) / (3 - (-5)) = (1) / (8) = 1/8

With the slope known, we choose one of the given points to find the y-intercept (b). Using the point-slope form of the equation (y - y1) = m(x - x1) with point (-5, -2) and slope 1/8:

y + 2 = (1/8)(x + 5)

y + 2 = (1/8)x + (5/8)

y = (1/8)x + (5/8) - 2

y = (1/8)x + (5/8) - (16/8)

y = (1/8)x - (11/8)

Therefore, the equation of the line is y = (1/8)x - (11/8), which corresponds to option 2.