The slope is change in "Y" divided by the change in "x"
1-(-3)/2-(-1)
= 4/3
Standard Form
y-y1=m(x-x1)
y-(-3)=4/3(x-(-1)
y+3=4/3x+4/3
y=4/3x-5/3
Rewrite in standard form
-4/3x+y=-5/3
Can't have fractions so multiply by 3 to get rid of the denominator
-4x+3y=5
Divide by -1 to get rid of the negative sign
4x-3y=-5
If you equate both, the y is eliminated:
-6x-3 = -x+2
Simplify this to find x:
-5x = 5
x = -1
Fill in x=-1 in either equation:
y = --1 + 2 = 3
So (-1,3) is the solution, it is where the lines intercept.
Answer: -1 < x < 8
x = 3
x ≠ 2
<u>Step-by-step explanation:</u>
Isolate x in the middle. Perform operations to all 3 sides.
-6 < 2x - 4 < 12
<u>+4 </u> <u> +4</u> <u>+4 </u>
-2 < 2x < 16
<u>÷2 </u> <u>÷2 </u> <u> ÷2 </u>
-1 < x < 8
**************************************************************************
Isolate x. Solve each inequality separately. Remember to flip the sign when dividing by a negative.
4x ≤ 12 and -7x ≤ 21
<u>÷4 </u> <u>÷4 </u> <u> ÷-7 </u> <u>÷-7 </u>
x ≤ 3 and x ≥ 3
Since it is an "and" statement, x is the intersection of both inequalities.
When is x ≤ 3 and ≥ 3? <em>when x = 3</em>
****************************************************************************
Isolate x. Solve each inequality separately.
15x > 30 or 18x < -36
<u>÷15 </u> <u> ÷15 </u> <u> ÷18 </u> <u>÷18 </u>
x > 2 or x < 2
Since it is an "or" statement, x is the union of both inequalities.
When we combine the inequalities, x is every value except 2.
x ≠ 2
(r^-7)^6 = r^-42 . . . . exponents are multiplied
This is a function, imagine if there were a line going up and down through every point, if one of those lines hits 2 points then it's not a function
