Slope-Intercept
Convert to slope-intercept form (y = mx + b): 3y = 6x + 9
Solution:
Divide all terms by 3
y = 2x + 3
Answer: y = 2x + 3
Convert y = 2x + 5 to standard form
Solution:
Subtract 2x from both sides
-2x + y = 5
Final answer: 2x - y = -5
Convert y = 2x + 3 to point-slope form using the point (1, 5)
Solution:
First identify that (1, 5) is a point on the line
Use the slope m = 2 from the original equation
Apply point-slope formula: y - y₁ = m(x - x₁)
y - 5 = 2(x - 1)
Which singer broke records in 2023 with her Eras Tour, which became the first tour to gross over $1 billion?
Taylor Swift
Convert to slope-intercept form: y - 4 = 5(x + 2)
Solution:
Distribute 5: y - 4 = 5x + 10
Add 4 to both sides: y = 5x + 14
Answer: y = 5x + 14
Convert y = -3x - 4 to standard form
Solution:
Add 3x to both sides
3x + y = -4
Final answer: 3x + y = -4
Convert y = -3x + 4 to point-slope form using the point (2, -2)
Solution:
Point is (2, -2)
Slope m = -3
Apply formula: y - (-2) = -3(x - 2)
Simplify to: y + 2 = -3(x - 2)
What 2023 movie starring Margot Robbie and Ryan Gosling dominated the box office and sparked a global pink fashion trend?
Barbie
Convert to slope-intercept form: 4x - 2y = 8
Solution:
Subtract 4x from both sides: -2y = -4x + 8
Divide all terms by -2
Answer: y = 2x - 4
Convert y - 1/2 = 4x to standard form
Solution:
Add 1/2 to both sides
y = 4x + 1/2
Subtract 4x from both sides
-4x + y = 1/2
Multiply all terms by 2 to eliminate fractions
Final answer: 8x - 2y = -1
Convert 2x - 3y = 12 to point-slope form using the point (0, -4)
Solution:
First solve for y: -3y = -2x + 12
y = (2x - 12)/3
Slope m = 2/3
Use point (0, -4)
y - (-4) = (2/3)(x - 0)
Simplify to: y + 4 = (2/3)x
Which artist released the album "For All The Dogs" in October 2023 and announced a surprise break from music shortly after?
Drake
Convert to slope-intercept form: 3(y + 1) = 2(x - 4) + 5
Solution:
Distribute on left side: 3y + 3 = 2x - 8 + 5
Combine like terms on right: 3y + 3 = 2x - 3
Subtract 3 from both sides: 3y = 2x - 6
Divide all terms by 3
Answer: y = (2/3)x - 2
Convert (x/3) + (y/2) = 4 to standard form
Solution:
Multiply all terms by 6 (LCM of 2 and 3) to eliminate fractions
2x + 3y = 24
Final answer: 2x + 3y = 24
Convert y = (x + 2)/(3) - 1 to point-slope form using the point (-3, -2)
Solution:
Multiply both sides by 3: 3y = x + 2 - 3
Solve for y: y = (1/3)x - 1/3
Identify slope m = 1/3
Use point (-3, -2)
y - (-2) = (1/3)(x - (-3)
Which K-pop girl group made history at Coachella 2023 as the first K-pop girl group to headline the festival?
BLACKPINK
Convert to slope-intercept form: 6(2y - 3) = 4(3x + 1) - 2
Solution:
Distribute on left side: 12y - 18 = 12x + 4 - 2
Combine like terms on right: 12y - 18 = 12x + 2
Add 18 to both sides: 12y = 12x + 20
Divide all terms by 12
Answer: y = x + 5/3
Convert (2x - 3)/(4) = y + 5 to standard form
Solution:
Multiply all terms by 4 to eliminate fraction
2x - 3 = 4y + 20
Subtract 4y from both sides
2x - 4y = 23
Final answer: 2x - 4y = 23
Convert 4x + 2y = 8 to point-slope form using the y-intercept and the point (3, -2)
Solution:
Find y-intercept by setting x = 0: 2y = 8 - 4(0), so y = 4
Now have two points: (0, 4) and (3, -2)
Calculate slope: m = (-2 - 4)/(3 - 0) = -6/3 = -2
Use point (3, -2)
y - (-2) = -2(x - 3)
Simplify to: y + 2 = -2(x - 3)
What video game, released in September 2023, broke records by selling over 40 million copies in 3 days and featured the voice acting of Laura Bailey as Yaara?
Starfield