SOLUTION: If a line has an x-intercept at x=4 and a y-intercept at y=-2 find its equation in the form y=mx+b.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: If a line has an x-intercept at x=4 and a y-intercept at y=-2 find its equation in the form y=mx+b.      Log On


   

Question 1204229: If a line has an x-intercept at x=4 and a y-intercept at y=-2 find its equation in the form y=mx+b.
Found 3 solutions by ikleyn, math_tutor2020, greenestamps:
Answer by ikleyn(52751) About Me  (Show Source):
You can put this solution on YOUR website!
.

Then b = -2  and m = %280+-+%28-2%29%29%2F%284-0%29 = 2%2F4 = 1%2F2,


so the equation is  y = %281%2F2%29x-2 = 0.5x - 2.    ANSWER

Solved.

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The solution to this problem requires no more than 2 lines.


If this solution in  2  lines does not convince you,  it is a bad signal:

    it means that you understand  highlight%28highlight%28NOTHING%29%29  in the subject.



Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

Method 1

The x-intercept always happens when y = 0.
The y-intercept always happens when x = 0.

This means an x-intercept of 4 and y-intercept of -2 produces the points (4,0) and (0,-2)

Let's find the slope of the line through them.




m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29

m+=+%28-2+-+0%29%2F%280+-+4%29

m+=+%28-2%29%2F%28-4%29

m+=+1%2F2
The slope is 1/2.
It means "go up 1, then right 2".

The y-intercept is b = -2 as mentioned earlier.

We will go from the template y = mx+b to the final answer y = (1/2)x - 2

This is the same as writing either y+=+%281%2F2%29x-2 or y+=+expr%281%2F2%29x-2

Optionally you could replace 1/2 with 0.5, but I don't think that slope is as helpful since 1/2 means "up 1, right 2". It might be tricky to convey that with 0.5

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Method 2

Let 'a' and b represent the x and y intercepts.
Neither value can be zero.

The aptly named intercept form is: x%2Fa+%2B+y%2Fb+=+1
This form allows us to quickly spot the x and y intercepts without having to do any math.

Since the x-intercept happens when y = 0, it leads to,
x%2Fa+%2B+y%2Fb+=+1

x%2Fa+%2B+0%2Fb+=+1

x%2Fa+%2B+0+=+1

x%2Fa+=+1

x+=+a%2A1

x+=+a
We have shown that when y = 0, it produces x = a.
Therefore the x-intercept is located at (a,0)
Similar steps will show that the y-intercept of x%2Fa+%2B+y%2Fb+=+1 is (0,b)

In this case a = 4 and b = -2
x%2Fa+%2B+y%2Fb+=+1

x%2F4+%2B+y%2F%28-2%29+=+1

x%2F4+-+y%2F2+=+1

4%2A%28x%2F4+-+y%2F2%29+=+4%2A1 Multiply both sides by the LCD 4 to clear out the fractions.

x-2y+=+4

-2y+=+4-x

-2y+=+-x%2B4

y+=+%28-x%2B4%29%2F%28-2%29

y+=+%28-x%29%2F%28-2%29%2B%284%29%2F%28-2%29

y+=+%281%2F2%29x+-+2
We arrive at the same answer found back in the previous method.

Answer by greenestamps(13195) About Me  (Show Source):
You can put this solution on YOUR website!


In the equation y=mx+b, b is the y-intercept, which we are given to be -2. So to find the equation in y=mx+b form, we only need to find the slope m.

I firmly believe students will enjoy math more if they understand what they are doing instead of plugging numbers into formulas. I have seen hundreds of cases where students got the wrong value for the slope because they plugged the wrong numbers in the wrong places in the slope formula.

To find the slope of the line from the given information, we need to determine the slope of the line through the two given points (0,-2) and (4,0). Instead of plugging numbers into the formula or slope, use the basic concept of slope = rise over run.

From (0,-2) to (4,0), the run is 4 and the rise is 2, so the slope is 2/4 = 1/2.

And so the equation of the line in y=mx+b form is

y = (1/2)x-2