Solve. Enter your answer as a mixed number. The driving distance from the sports arena to Kristina's house is 11 7 10 miles. The
1 answer:
Answer:
Step-by-step explanation:
From the sports arena to Kristina's house =
From the sports arena to Luke's house =
Subtract Luke from Kristina
There's a confusing but easy way to solve this. However, I'm going to convert into improper fractions to make it easier.
To convert to improper fraction, take the whole number, multiply it by the denominator and add it to the numerator. All over the same denominator.
Subtract them.
Convert to mixed number by dividing.
65/10=6
60
----
5
The 6 is the whole number, 5 the numerator and 10 the denominator. Remember the negative sign that we had.
5 and 10 can be simplified
5/5=1
10/5=2
Our final answer would be:
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Answer:
Step-by-step explanation:
Given
Required
Determine the difference between the points
The difference is calculated as follows:
Answer:
Step-by-step explanation:
The equation of a line is y = mx + b
Where:
- m is the slope
- b is the y-intercept
First, let's find what m is, the slope of the line.
Let's call the first point you gave, (-3,1), point #1, so the x and y numbers given will be called x1 and y1.
Also, let's call the second point you gave, (2,-1), point #2, so the x and y numbers here will be called x2 and y2.
Now, just plug the numbers into the formula for m above, like this:
So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:
Now, what about b, the y-intercept?
To find b, think about what your (x,y) points mean:
- (-3,1). When x of the line is -3, y of the line must be 1.
- (2,-1). When x of the line is 2, y of the line must be -1.
Now, look at our line's equation so far: .
is what we want, the -
is already set and x and y are just two 'free variables' sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (-3,1) and (2,-1).
So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!
You can use either (x,y) point you want. The answer will be the same:
- (-3,1). y = mx + b or
, or solving for b:
.
.
- (2,-1). y = mx + b or
, or solving for b:
.
See! In both cases, we got the same value for b. And this completes our problem.
The equation of the line that passes through the points (-3,1) and (2,-1) is