The pair of points (6, y) and (10, –1) lie on a line with slope one-fourth. What is the value of y?
(1 point)
Responses
–5
–5
–2
–2
2
2
5
To find the value of y, we can use the formula for finding the slope between two points (x₁, y₁) and (x₂, y₂):
slope = (y₂ - y₁) / (x₂ - x₁)
In this case, the slope is given as one-fourth and the points are (6, y) and (10, -1).
So, substituting the values into the formula:
1/4 = (-1 - y) / (10 - 6)
Multiplying both sides by (10 - 6) gives:
1 = (-1 - y) / 4
Multiplying both sides by 4 gives:
4 = -1 - y
Subtracting 1 from both sides gives:
y = -5
Therefore, the value of y is -5.
To find the value of y, we can use the formula for slope:
slope = (change in y) / (change in x)
The given slope is one-fourth. We can use the points (6, y) and (10, -1) to find the change in y and change in x.
change in y = -1 - y = -1 - y
change in x = 10 - 6 = 4
Plugging these values into the formula for slope, we get:
1/4 = (-1 - y) / 4
Cross-multiplying:
4*(-1 - y) = 4 * 1/4
-4 - 4y = 1
Adding 4 to both sides:
-4 - 4y + 4 = 1 + 4
-4y = 5
Dividing both sides by -4:
-4y / -4 = 5 / -4
y = -5/4
Therefore, the value of y is -5/4.