What’s the equation of a line on a graph with points of (3,-3) (-2,2)?
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Y=mx*c Sub gives -3=3m+c Also 2=-2m+c Subtract both equations You get 5=-5m So m=-1 Sub into either equation C=0 Therefore y=-x Is equation of the straight line which is very clear from the points coordinates!
Shanice St John
A maths enthusiast.
To find the equation of a straight line, we need to find the following information: 1) The gradient (denoted by the symbol, m) 2) The y-intercept (denoted by the symbol, c) To find the gradient of the line, we need to use the following equation: m = (y2 - y1)/(x2 - x1) , where (x1,y1) and (x2,y2) are two given coordinates. Let (x1,y1) = (3,-3) and (x2,y2) = (-2,2). Note that: The values that are assigned to the given coordinates does not make a difference to the answer that be obtained for m. For instance, assigning (x1,y1) as (-2,2) and (x2,y2) as (3,-3) will not change the value of m. Once the values of x1, y1, x2 and y2 are chosen, keep them unchanged throughout the calculation; consistency is key. Now substituting in the values of x1= 3, y1= -3, x2= -2 and y2= 2 into the equation for m (the gradient) yields: m = (y2 - y1)/(x2 - x1) = (2 - -3)/(-2 - 3) = (2 + 3)/(-2 - 3) (- and - make a +) = 5/-5 = -1 Now considering the form of a straight line equation: y = mx + c We know that m = -1 including the coordinates of the two points. To find c (the y-intercept), we can substitute the value of m and any of the two coordinates (as they both lie on the graph of the straight line). Substituting in m = -1 and the coordinates (3,-3), we find the value of c to be: y = mx + c -3 = -1(3) + c -3 = -3 + c (Add ‘3’ to both sides.) -3 + 3 = -3 + 3 + c 0 = 0 + c c = 0 Therefore, the equation of the line passing through points (3,-3) and (-2,2) is: y = (-1)x + 0 y = -x (This is the final answer.) I hope this helps.
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