Question

The slope of a line that passes through points (5, 14) and (-4, y) is 4/9. What is the value of y?​

Answer 1

Answer: y = 10

Step-by-step explanation:

The slope of a line is the rise/run, so if you want to find the slope of a line between two points, you can take the change in y between the two points and divide it by the change in x.

The change in y would be (y2 - y1), where y2 is the y position of the second point and y1 is the y position of the first.

In a similar manner, to find the change in x, we can use (x2 - x1), where x2 is the x position of the second point and x1 is the x position of the first.

Now that we have the change in x and the change in y, we can make an equation to find the slope (which is change in y / change in x):

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

Now we can assign the points:

Point 1 is (5, 14)

Point 2 is (-4, y)

(Note: You could flip which point is which, and it wouldn't change the final answer, I'm just assigning these so you know where the x and y values are coming from when I plug the values into the equation)

Now that we have both points, we can plug the values into the equation:

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

m = (y - 14) / (-4 - 5)

m = (y - 14) / (-9)

There's one piece of information we haven't used yet, which will help us solve for the value of y. What we need to use is the slope (which is given to us as 4/9).

Plugging in the value of the slope will let us get y:

m = (y - 14) / (-9)

4/9 = (y - 14) / (-9)

-4 = (y - 14)

(Note: We're multiplying both sides by -9, don't forget about the negative sign)

-4 = y - 14

y = -4 + 14

y = 10

Answer 2

Answer:

slope=m=4/9

(x',y')=(5,14)

(x",y")=(-4,y)

we have

m=(y"-y')/(x"-x')

4/9=(-4-5)/(y-14)

4y-56=-81

4y=-81+56

y=-25/4