From Standard Form to Slope-Intercept
The journey to a more useful line equation!
First Things First
Homework Take Up
Graph This!
Let’s graph a couple of lines:
y = 2x - 3 And 6x - 3y - 9 = 0
Slope (m) = 2 x-int: Sub y=0 y-int: Sub x=0
y-int = -3 6x - 3(0) - 9 = 0 6(0) - 3y - 9 = 0
That’s all 6x = 9 -3y = 9
we need! x = 9/6 = 3/2 y = -3
That’s all we need!
Graph ‘Em Both!
First graph y = 2x - 3 using the y-intercept and slope
Then graph 6x - 3y - 9 = 0 using the x-intercept of 3/2 and y-intercept of -3
They’re the same line! <:-O
It turns out that the second line 6x-3y-9=0 is in standard form and is equivalent to y=2x-3.
What is standard form?
Standard form is just another way to represent a line. What makes it standard form?
Held to a Higher Standard Form
Which of the following are in standard form?
a) 2x - 3y + 5 = 0 b) 2y - 3x = 6
c) 1 x - 7y + 21 = 0 d) 8x - 9y + 10 = 0
4
e) -x + 2y - 1 = 0 f) x + 18y - 36 = 0
g) 5x + 3 y - 6 = 0 h) 10x + 2y - 14 = 0
2 17
Convert
It is often easier to graph a line when it is in slope-intercept form (y=mx+b). To do this, we will need to convert the line from standard form to slope-intercept form.
Ax + By + C = 0 =====> y = mx + b
But how?
Isolation is the Key
We need to isolate y from standard form in order to find slope-intercept form:
I’m All Alone! There’s No one here beside Y!
Lets try it with the example from earlier:
6x - 3y - 9 = 0
-6x +9 -6x +9
-3y = -6x + 9
-3 -3 -3
y = 2x - 3
Notice that this is the same as the other equation!
Try, Try again!
Convert the following into y = mx + b form:
a) 4x - 3y + 12 = 0
-3y = -4x - 12
y = 4 x + 4
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ALWAYS REDUCE YOUR FRACTIONS
b) 24x+12y+48=0
12y = -24x-48
y = -2x - 4
Try For Yourself
Determine the slope and y-intercept, then check with a partner.
a) 3x + 5y - 15 = 0 b) 2x - 9y + 27 = 0
Practice/Homework