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A line passes through (2,-1) and (5,y). Find the value of y if the slope of the line is 3.

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2 Answers

Use the slope definition as the ratio of the change of y to the change of x,

(y+1)/(5-2) = 3

Multiply both sides by 3,

y+1 = 9

Add -1 to both sides,

y = 8 <==Answer

I'll try breaking it down a different way.
If you find the formula for the line that these points are on, you can then plug any x-coordinate and receive it's y-coordinate.
Here, you're given two points that are on a single line.
The formula for a line is y = mx + b      
m is the slope , b is the y-intercept
You're given the slope m already. It's 3. And you have points for y and x.
Now you need to slove for b. 
Plug in your first full point (2,-1) => -1 = 2(3)+b
Solving for b = -1 - 2(3) = -7
Now we have our linear formula: y = 3x - 7
Now we can plug the x-coordinate of our next point (5,y) and we will get the y-coordinate
y = 3(5) - 7 = 15 - 7 = 8
y = 8  <= that's your answer