I cannot remember how to find the slope of a line when you are given two points.

Here is the problem.

The slope of a line through (2,1) and (5,n) is 3. n=___

I ended up with -2. But I don't think that is the right answer. I put the points in slope-intercept form and solved for y, which would end up being n, right?
y(or n)=5x+3
y(1)=2x+3 [x equals -1 right?]

I'm so confused. . . .

How would you find slope if you knew all of the two points

just set

(n-1)/(5-2)=3
n-1 = 9
n = 10

test is by finding the slope, it works

the method you tried will work, but you made an error.

here is how it would have looked:

let y = mx + b, but we have a point (2,1) and m=3
1 = 3(2) + b
b = -5

so the equation is y = 3x - 5

now sub in (5,n)
n = 3(5) - 5
n = 10

much longer and more complicated, you must agree.

To find the slope of a line when you are given two points, you can use the formula:

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

Let's use the given points (2,1) and (5,n) to find the slope:

slope = (n - 1) / (5 - 2)

We are also given that the slope is 3:

3 = (n - 1) / (5 - 2)

To solve for n, we can cross-multiply:

3(5 - 2) = n - 1

9 = n - 1

To isolate n, we can add 1 to both sides:

n = 9 + 1

n = 10

Therefore, the value of n is 10.

To find the slope of a line when you are given two points, you can use the formula:

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

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Let's solve the problem step by step to find the value of n.

Given points: (2, 1) and (5, n)

Step 1: Substitute the coordinates into the slope formula:
m = (n - 1) / (5 - 2)

Step 2: Since the slope is given as 3, we can set up an equation:
3 = (n - 1) / (5 - 2)

Step 3: Simplify the equation:
3 = (n - 1) / 3

Step 4: Cross-multiply:
3(n - 1) = 3 * 3

Step 5: Distribute and simplify:
3n - 3 = 9

Step 6: Add 3 to both sides of the equation:
3n = 12

Step 7: Divide both sides of the equation by 3:
n = 4

So, the value of n is 4.

It seems like there was a mistake in your calculation. Instead of directly substituting the points into the slope-intercept form equation, you should first calculate the slope using the formula and then solve for n. In this case, the correct value of n is 4, not -2.