So remember that slope-intercept form is y = mx+b (m = slope, b = y-intercept) and standard form is ax+by = c. (a and b are coefficients and c is the constant)
Starting with the first question: 9x + 2y = 6
Firstly, subtract 9x on both sides: 2y = -9x + 6
Next, divide both sides by 2, and your equation will be y = -4.5x + 3
Now with the next equation: y - 3 = 4(x + 1)
Firstly, foil 4(x + 1): y - 3 = 4x + 4
Next, subtract y on both sides: -3 = 4x - y + 4
Next, subtract 4 on both sides, and your answer will be: -7 = 4x - y
Next equation: y + 7 = -2(x - 3)
Firstly, foil -2(x - 3): y + 7 = -2x + 6
Next, subtract 7 on both sides of the equation, and your answer will be: y = -2x - 1
Next: y - 5 = 3(x - 2) (part a)
Firstly, foil 3(x - 2): y - 5 = 3x - 6
Next, add 5 on both sides, and your equation is: y = 3x - 1
Next, y - 5 = 3(x - 2) (part b)
Firstly, foil 3(x - 2): y - 5 = 3x - 6
Next, subtract y on both sides of the equations: -5 = 3x - y - 6
Next, add 6 on both sides of the equation, and your answer will be: 1 = 3x - y
