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.