The pair of points (6, y) and (10, –1) lie on a line with slope . What is the value of y?
(1 point)
Responses
–5
–2
2
5
To find the value of y, we need to calculate the slope using the given points. The formula to find the slope (m) of a line passing through two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
Let's substitute the given points into the formula:
m = (-1 - y) / (10 - 6)
Simplifying the equation, we have:
m = (-1 - y) / 4
The slope is given as 2, so we can set it equal to the equation we found:
2 = (-1 - y) / 4
Now, let's solve for y by cross multiplying:
8 = -1 - y
Adding y to both sides, we have:
y + 8 = -1
Subtracting 8 from both sides, we get:
y = -1 - 8
y = -9
Therefore, the value of y is -9.
WRONG ITS -2
Apologies for the error. I made a mistake in my calculation.
Using the given points (6, y) and (10, -1) and the formula for calculating the slope, we have:
m = (-1 - y) / (10 - 6) = (y + 1) / 4
Since the slope is given as 2, we can set up the equation:
2 = (y + 1) / 4
Now, multiplying both sides by 4:
8 = y + 1
Subtracting 1 from both sides:
7 = y
Therefore, the value of y is 7.
To find the value of y, we first need to determine the slope of the line using the given points.
The slope of a line is calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
Let's plug the values of the given points into the formula:
slope = (-1 - y) / (10 - 6)
Next, we use the given slope and set it equal to the calculated slope:
slope = -2 / 4
Now, we can solve for y by substituting the slope value:
-2 / 4 = (-1 - y) / (10 - 6)
To simplify the equation, we can cross multiply:
-2 * (10 - 6) = 4 * (-1 - y)
-2 * 4 = -4 - 4y
-8 = -4 - 4y
To isolate y, we can add 4 to both sides of the equation:
-8 + 4 = -4 -4y + 4
-4 = -4y
Finally, we can solve for y by dividing both sides of the equation by -4:
y = -4 / -4
y = 1
Therefore, the value of y is 1.