The pair of points (−6, y) and (4, 8)
lie on a line with a slope of 5/2
.
The slope of a line that passes through two points (x1,y1) and (x2,y2) can be calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
You have provided the slope of the line as 5/2 and one pair of points (4, 8). Using the given point (4, 8) as (x2, y2) and the point (−6, y) as (x1, y1), we can plug these values into our slope formula.
Given:
slope = 5/2
x1 = -6
y1 = y (unknown)
x2 = 4
y2 = 8
Using the slope formula:
5/2 = (8 - y) / (4 - (-6))
Now let's solve for y step-by-step:
5/2 = (8 - y) / (10)
Now, cross-multiply to get rid of the fraction:
5 * 10 = 2 * (8 - y)
50 = 16 - 2y
Now, we want to isolate y on one side of the equation:
50 - 16 = -2y
34 = -2y
Now divide both sides by -2 to solve for y:
34 / -2 = y
y = -17
Thus, the y-coordinate for the point (-6, y) is -17. So the complete coordinate of the point that lies on the line with a slope of 5/2 and through the point (4, 8) is (-6, -17).