1. 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
Question
- 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
Solution
Sure, here are the solutions to your problems:
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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, m = (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 (12, 21) and m = 7, we get c = 21 - 7*12 = -63. (iii) The equation of the line is therefore y = 7x - 63.
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To solve the equation 7x – 5 = 33, add 5 to both sides to get 7x = 38, then divide both sides by 7 to get x = 38 / 7 = 5.43 (rounded to two decimal places
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