Which of the following equations is 2x + 3y = 6 written in slope-intercept form.
2 answers:
Answer:
The equation
Step-by-step explanation:
Equations of the form are known as Standard Form for a linear equation in two variables, x and y, in the case of your equation
where a = 2, b = 3 and c = 6.
Equations of the form are known as Slope-Intercept form. This is called in this way because
is equal to the slope of the line, and
is the value of y when x = 0, which makes it the y-intercept.
To convert from standard form to slope-intercept form
, we need to follow these steps:
- Subtract 2x from both sides
- Simplify
- Divide both sides by 3
- Simplify
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You can get all the terms on one side, and then solve for x by any means:
Factor out a -2:
Factor this equation:
I will use the AC method. To use it, first multiply a and c (in ax^2 + bx +c):
Now, look for two numbers that multiply to -12 and add to -11. Obviously these numbers are -12 and 1. (-12*1 = -12 and -12+1 = -11). Now, because of rules, you set it up in a Punnett square:
4x^2 -12x
x -3
Now, we find common factors of the terms in rows:
_x_______-3__
4x| 4x^2 -12x
1 | x -3
So, you can use this to write an equivalent expression to the quadratic given:
Now, we known the factors are (solve for x): 3 and -1/4.
Factor out a -2:
Factor this equation:
I will use the AC method. To use it, first multiply a and c (in ax^2 + bx +c):
Now, look for two numbers that multiply to -12 and add to -11. Obviously these numbers are -12 and 1. (-12*1 = -12 and -12+1 = -11). Now, because of rules, you set it up in a Punnett square:
4x^2 -12x
x -3
Now, we find common factors of the terms in rows:
_x_______-3__
4x| 4x^2 -12x
1 | x -3
So, you can use this to write an equivalent expression to the quadratic given:
Now, we known the factors are (solve for x): 3 and -1/4.