This equation is called a "y-intercept form":
y = mx + b
y is just a y variable
m is called the slope
x, just like y, is just an x variable
b is the "y intercept" (the point where the line passes the y axis)
To have this equation work, you only need TWO components:
m and b (slope and the y intercept)
Let's find the y intercept form of the example below, (see the first picture): **note: refresh the page**
Recall that you need to find two components, m and b.
Let's find b first because it is the easiest.
As you can see, the line in the pic passes the point (0,5) or 5
So b = 5
y = __x + 5
Note: If the line passes through point (0,-5) for instance, the b value would be negative. b = -5
Now that we found the y intercept (or b), we find the slope (m).
Take two good and clear points coordinates that is in the line.
In the picture, I'll take these points:
(-10,0) and (0,5)
Now remember this formula (I know it is hard but it is important):
m = y₂ - y₁ / x₂ - x₁
Where,
y₂ = 5
y₁ = 0
x₂ = 0
x₁ = -10
Now that there is a formula and two points, we can solve for the slope.
m = 5 - 0 / 0 - (-10)
m = 5 / 0 + 10
m = 5 / 10
m = 1/2
Now that we have m and b, we have finally completed the y intercept form.
y = __x + __
y = mx + b
y = 1/2x + 5
__x + __y = __
What is this equation you might say?
This is called a standard form of equation of a line.
How to make an equation y = __x + __ when it looks like __x + __y = __
Let's take our equation again.
y = 1/2x + 5
We just need to rearrange the equation to make it standard. Look carefully.
y = 1/2x + 5
-1/2x + y = 5
...And that's it basically.
If you were to make standard form to y intercept, rearrange.
2x + 1/2y = 10
1/2y = -2x + 10
Now you can't have 1/2y so you multiply all sides by 2.
1/2y = -2x + 10
y = -2x · 2 + 10 · 2
y = -4x - 20
Equal Value Equation.
You are to face a hard question.
Q: What point does y = 1/2x + 5 intersect with y = 2x - 10
A: IDK I DID NOT STUDY FOR THIS :(((((((
This is rather simple.
Here are the steps:
Set the two equations together.
y = 1/2x + 5
y = 2x - 10
Now remove the "y ="
1/2x + 5
2x - 10
Now here is what you do next, put the equations together as equal.
1/2x + 5 = 2x - 10
Now at this point, you have to solve for x.
**1/2x = 0.5x to make it more easier to read**
0.5x + 5 = 2x - 10
0.5x - 2x + 5 = -10
-1.5x + 5 = -10
-1.5x = -10 - 5
-1.5x = -15
x = -15 ÷ -1.5
x = 10
(10,__)
Now we have found x, we find y by substituting the x on one of the equations.
I'll take this, y = 2x - 10
Substitute then solve.
y = 2(10) - 10
y = 20 - 10
y = 10
(10,10)
Now the equations y = 1/2x + 5 and y = 2x - 10 intersect at (10,10)
The graph in the second picture proves that this is correct.
Okay! Now you might have understood it now. If you still did not understand the Equal Values Equation then copy and paste the link in the comment of this answer.
Took me a while to do this but I am determined to help you in this test.
Cheers and Good Luck on your test :)
