Using intercepts
Find the intercepts for 3x-2y=6
To find the x-intercept, Replace Y with 0 and solve for x
step 1) 3x-2(0)= 6
step 2)3x-6
step 3)x=2
the X-intercept is 2
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To find the y-Intercept, Replace x with 0 and solve for Y
step 1)3(0)-2y=6
step 2)-2y=6
step 3)y=-3
The Y-intercept is -3
solve
5x2+2x-1 and 4x2-x+2
(5x2+2x-1)+(4x2-x+2)
Rewrite the problem, Vertically aligning the terms
5x2+2x-1
+4x2-1x+2
_________
9x2+1x+1
simplify--
9x2+x+1
Solve-
(x2+5)-(2x2-1)
step 1)Distribute the negative
(x2+5)-(2x2-1)
=x2+5-2x2-(-1)
=x2+5-2x2+1
step 2) Combine like terms
x2+5-2x2+1
=-x2+6
solve- (3x+5)(2x-7)
F O I L
(3x)(2x)+(3x)(-7)+(5)(2x)+5(-7)=
6x2-21x+10x-35=
6x2-11x-35
what is linear equation formals
1) slope intercept Y=MX+B
2) point slope Y-Y1=M(X-X1)
3) standard Ax+By=C
4) intercept form X/A+ Y/B=1
Write the equations in standard form
3/4x+1/2y+3
X-intercept
step 1) 3/4x+1/2(0)=3
step 2)3/4x=3
x=4
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Y-intercept
step 1)3/4(0)+1/2y=3
step 2) 1/2y=3
y=6
solve
3y3+2y+1 and y2-1
(3y3+2y+1)+(y2-1)
Rewrite the problem, Vertically aligning the terms
3y3+(0)y2+2y+1
+0y3+ 1y2+0y+-1
___________________
3y3+1y2+ 2y+0
simplify
3y3+2y2+2y
solve in standard form
(3x2-5)+(2x2-4x-1)
step 1)3x2-5+2x2-4x-1
step 2) 3x2+2x2=5x2
step 3) -5+-1=6
step 4)5x2-5x-6
solve FOIL
(5x+2)(2x-7)
F O I L
5x(2x) 5x(-7) 2(2x) 2(-7)
10x2- 35x + 3x - 14
___________________________
10x2-31x-14
M=y2-y1/x2-x1=4-(-2)/3-0=6/3=2
y-y1=m(x-x1)
Y-4=2(x-3)
Solve 2x+4y=8
X-intercept
step1) let y=0
step2) 2x+4y=8
step3)2x+4(0)=8
step4) 2x+0=8
step5) 2x/2 = 8/2
step6) x=4
The x-intercept (4,0)
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Y-intercept
step1)let x=0
step2) 2x+4y=8
step3) 2(0)+4y=8
step4) 0+4y=8
step5) 4y/4 +8/4
step6)y=2
The Y-intercept is (0,2)
solve
5x2+2+1 and -4x2-x-2
(5x2+2x+1)+(-4x2-x-2)
=(5x2-4x2)+(2x-x)+(1-2)
=x2+x-1
Solve (5x2-9x+11)-(-2x2+3x-2)
step 1) (5x2-9x+11)+(+2x2-3x+2)
step 2) (5x2+2x2)+(-9x-3x)+(11+2)
step 3) (7x2)+(-12x)+(13)
= 7x2-12x-13
solve (2x-1)3=(2x-1)(2x-1)(2x-1)
=(2x-1)(4x2-2x-2x+1)
=(2x-1)(4x2-4x+1)
=8x3-8x2+2x-4x2+4x-1
=8x3-12x2+6x-1
solve- 8x-4y=4 and 2x=6
A)8x-4y=4
-----------------
8x-4y=4
-4y=-8x+4
y=2x-1
__________________________________________
B)2x=6
--------
2x=6
x=3
Solve -5x+6y=60
To find the X-intercept, Replace Y with 0 and solve for x
step 1) -5x+6(0)=60
step 2)-5x=60
x=-12
The x-intercept is -12
__________________________________________
To find the Y-intercept, replace x with 0 and solve for Y
step 1)-5(0)+6y=60
step 2)6y=60
y=10
The y-intercept is 10
solve- (6x2+3x-4)+(x2-7)
6x2+3x-4
+ x2+ -7
____________
7x2+3x-11
solve- (-63+5x2-3)-(2x3-4x2-3x+1)
-6x3+5x2+0x-3
+ -2x3+4x2+3x-1
___________________
-8x3+9x2+3x-4
solve (a-4a3+a5-8)+(-9a5+a4-7a+5+a3
=a-4a3+a5-8-9a5+a4-7a+5+a3
=-8a5+a4-3a3-6a-3
solve
(-1,3) (2,-5)
1)m=y2-y1/x2-x1 -5-3/2-(-1) = -8/3
2) y-y1=m(x-x1)
y-(-5)=-8/5 (x-2)
=-8/3x+16/3=15/3
y=-8/3x+1/3
Write the equations in standard form
-12x+18y=108
x-intercept
step 1)-12x+18(0)=108
step 2)-12x=108
x=-9
__________________________________________
y-intercept
step 1)-12(0)+18y=108
step 2) 18y=108
y=6
solve
-ab+b and ab-a
(-ab+b)+(ab-a)
=(-ab+ab)+b+(-a)
=b-a
solve (2x2-3x+1)-(x2+x+1)
step 1)(2x2-3x+1)+(-x2-x-1)
step 2) (2x2-3x+1)+(-x2-x-1)
step 3) (2x2-3x+1)+(-x2-x-1)
2x2-3x+1
-x2-x-1
_____________
x2-4x
solve
(2x+3)-(5+7)=(2x+3)+(-1)(5x+)
=2x+3+(-1)(5x)+(-1)(7)
=2x+3+(-5x)+(-7)
=2x+(-5x)+3+(-7)
=(-3x)+(-4)
=-3x-4
solve
E(-3,7)
F(6,-5)
7- -5/-3-6=7+5/-3-6=12/-9=-4/3
Y=MX+B
-5=-4/3 (6)/1+b
-5=-8+b
3=b
Y=-4/3x=3