How does the mindset affect the ability to successfully translate figures?

Here is an example this is NOT the answer

Step-by-step explanation:

You want to find the equation for a line that passes through the two points:

(3,1) and (0,2).

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

First, let's find what m is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. 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. Or, x1=3 and y1=1.

Also, let's call the second point you gave, (0,2), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=0 and y2=2.

Now, just plug the numbers into the formula for m above, like this:

m=  

2 - 1

0 - 3

or...

m=  

1

-3

or...

m=-1/3

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y=-1/3x+b

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.

(0,2). When x of the line is 0, y of the line must be 2.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=-1/3x+b. b is what we want, the -1/3 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 (0,2).

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 1=-1/3 × 3+b, or solving for b: b=1-(-1/3)(3). b=2.

(0,2). y=mx+b or 2=-1/3 × 0+b, or solving for b: b=2-(-1/3)(0). b=2.

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 (0,2)

is

y=-1/3x+2