Question

HELP PLS
What is the slope of the line that passes through (1, 4) and (-3, -3)?

Answer 1

y=7/4x+9/4

Explanation:

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

(1,4) and (-3,-3).

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, (1, 4), point #1, so the x and y numbers given will be called
`x_1` and
`y_1`. Or,

Also, let's call the second point you gave, (-3,-3), point #2, so the x and y numbers here will be called
`x_2` and
`y_2`. Or,

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

m=

`(-3-4)/(-3-1)`

m= 7/4

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=7/4x+b

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

(1,4). When x of the line is 1, y of the line must be 4.

(-3,-3). When x of the line is -3, y of the line must be -3.

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

Now, look at our line's equation so far: y=7/4x+b. b is what we want, the 7/4 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 specifically passes through the two points (1,4) and (-3,-3).

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:

(1,4). y=mx+b or 4=7/4 × 1+b, or solving for b: b=4-(7/4)(1). b=9/4.

(-3,-3). y=mx+b or -3=7/4 × -3+b, or solving for b: b=-3-(7/4)(-3). b=9/4.

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

(1,4) and (-3,-3)

is

y=7/4x+9/4