A line passes through coordinates (-2,4) and (8,9). Does the point with coordinates (32,55) fall on this line?

To work out if a given point with coordinates (X,Y) falls on a line you must work out the equation for the line. All straight lines follow the formula: y=mx+c with 'y' being the Y coordinate, 'x' being the X coordinate, 'm' being the gradient (steepness) of the line, and 'c' the point at which the line crosses the Y-axis (Y-intercept).

You can calculate the gradient of a line if you have two points, in this case (-2,4) and (8,9), using the formula: (y2-y1)/(x2-x1) = (9-4)/(8--2) = 5/10 = 1/2. Therefore the gradient is 1/2. m=1/2. Placing this in our formula for the line gives y=(1/2)X + C

Next we need to calculate the value of 'C', where the line crosses the Y-axis. We already have 2 points on this line and can use either of them to work out the value of C. This is because the point's coordinates give us the values of X and Y. Putting the coordinates (-2,4) into the formula Y=(1/2)X + C gives 4=(1/2)(-2) + C. simplifying this gives 4 = -1 + C. Rearranging this we can see that C= 5.

This gives us our formula for the line: y = (1/2)x + 5

To see if a point (32,55) falls on the line, place it's X coordinate into the line eqution we have just calculated. y=(1/2)(32) + 5. which gives us y=16+5. Which gives us y=21. As the Y coordinate of the point given (55) does not match the value of Y from the line calculation (21), we can conclude that the point (32,55) does NOT fall on the line.