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This Lesson (HOW TO find equations, slopes and intercepts of straight lines) was created by by longjonsilver(2297)
  About longjonsilver: I have a new job in September, teaching
There are only a few types of questions that we can ask to test your knowledge of straight lines and coordinates. Here they are:
1. Find the equation of the line given 2 points EXAMPLE: Given points (-1,4) and (2,13), find the equation of the straight line that passes through them. solution: We know the equation will be of the form y=mx+c, so we just need to find the gradient, m and the y-intercept, c. These are simple enough exercises. Gradient, m = m = m = 9/3 m=3 so, we have y=3x+c now. To find c, we need to know x and y. Well, we do. We know 2 sets of x and y...the coordinates in the question, so just pick one pair and put them in the equation to find c...I will choose (-1,4): 4 = 3(-1) + c 4 = -3 + c --> c = 7 so the equation is y=3x + 7. Check now with your other pair of coordinates. Put the x-value in and see if the y-value you calculate matches that in the question: when x=2, y=3(2) + 7, so y=6+7 ie y=13, which is correct. So we KNOW the answer is correct. 2. Find the equation of the line given 1 point and the gradient EXAMPLE: Find the equation of the straight line that passes through point (3,4) and has a gradient of -5. solution: This is a lot simpler than the previous example, since we already know the gradient - no need to calculate it. Starting with y=mx+c, put in the information we know, namely, x,y and m... 4 = -5(3) + c 4 = -15 + c --> c = 19 so the equation is y=-5x+19 3. Find the gradient and y-intercept of a given straight line EXAMPLE: Find the gradient and y-intercept of the equation 3y + 12x - 7 = 0. solution: We need the equation in the y=mx+c form, so we need to re-arrange it. 3y + 12x - 7 = 0 --> add 7 to both sides 3y + 12x = 7 --> subtract 12x from both sides 3y = -12x + 7 --> now divide everything by 3 This is the same equation, but in the correct form, to tell us the gradient and y-intercept, ie gradient = -4 y-intercept = 7/3 This lesson has been accessed 111757 times. |
