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All lines, or linear functions, can be expressed as y=ax+b, where a is the slope or gradient and b the y intercept. To find out what the linear function is we use the values for x and y of two points on the line. So we have x=5 and y=175,  and x=8 and y=190. We can find a and b by solving two simultaneous equations: 175=5a+b and 190=8a+b. By subtracting one equation from the other we eliminate b and then we can find a: 15=3a so a=5.  Now substitute a=5 in one of the equations: 175=25+b, 150=b, so b=150. Check the other equation still balances: 190=40+150, which is true. So the equation is y=5x+150, and the y intercept is 150 (when x=0).

Another way to solve is to find the gradient, a, by dividing the difference of the y values of the two points by the difference between the x values: a=(190-175)/(8-5)=15/3=5. We find the intercept using the equation b=y-ax and we simply substitute the coordinates of one point for x and y and put in the value of a we just found.

by Top Rated User (608k points)
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