. Given two points (12 , 21) and (10 , 7):Determine the(i) gradient(ii) intercept(iii) State the equation of the line2. 7x – 5 = 33. 23 𝑥 = −84. 3(2𝑥 − 4) + 9 = 155. 1.75x + 4 = 6.26. Y + 15 = 1057. Rearrange the following equation to y = mx + c the following equation 2y = 4x - 6Do not submit as word file. Submit as PDF file

Sure, let's solve these step by step:

1. Given two points (12 , 21) and (10 , 7):

(i) The gradient (m) of a line is given by the formula (y2 - y1) / (x2 - x1). So, substituting the given points into the formula, we get (21 - 7) / (12 - 10) = 14 / 2 = 7.

(ii) The y-intercept (c) of a line is given by the formula y - mx = c. Substituting one of the points and the gradient into the formula, we get 21 - 7*12 = -63.

(iii) The equation of the line is therefore y = 7x - 63.

2. To solve the equation 7x – 5 = 3, add 5 to both sides to get 7x = 8, then divide both sides by 7 to get x = 8/7.

3. To solve the equation 23x = -8, divide both sides by 23 to get x = -8/23.

4. To solve the equation 3(2x - 4) + 9 = 15, first distribute the 3 to get 6x - 12 + 9 = 15, then simplify to get 6x - 3 = 15. Add 3 to both sides to get 6x = 18, then divide both sides by 6 to get x = 3.

5. To solve the equation 1.75x + 4 = 6.2, subtract 4 from both sides to get 1.75x = 2.2, then divide both sides by 1.75 to get x = 2.2 / 1.75 = 1.257.

6. To solve the equation Y + 15 = 105, subtract 15 from both sides to get Y = 90.

7. To rearrange the equation 2y = 4x - 6 to the form y = mx + c, divide every term by 2 to get y = 2x - 3.

I'm sorry, but I can't assist with that.