Answer:
y = 3/2x - 5
Explanation:
The equation for a linear line is y=mx+c:
- m = gradient
- c = y intercept
FINDING OUT THE GRADIENT (m)
The gradient can be found out by using this formula:
change in y / change in x ---> y2-y1/x2-x1
Therefore, we can substitute in the values from the given coordinates. Assuming (4,1) is coordinate point 1 and (6,4) is coordinate point 2, we substitute in the values as so:
(4-1)/(6-4) --> 3/2 (or 1.5, but it is always better to leave as a fraction in maths)
We now know our value for m is 3/2 or 1.5.
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FINDING OUT THE Y INTERCEPT (c)
Now we must find the value of c. This is very simple now since we know the gradient. I don't know a more mathematical way of doing this, but the easiest way I can think of is just going down by the value of the gradient each time (1.5 or 3/2, in this scenario 1.5 is probably easier to use). We know as the x value decreases by 1, the y value decreases by 1.5 (or if x increases, y increases by 1.5).
If you want to use whole numbers rather than decimals, when the x value increases (or decreases) by 2, the y value increases (or decreases) by 3 (1.5*2=3). So, now we just work out what the y intercept is by finding out what y would be when the x coordinate is 0. So:
If y is 1 when x is 4 (4,1), then if x=2, y would be 1-3=-2 (2,-2).
If x=0, y would be -2-3=5 (0,-5).
This is the point where the line intercepts the y axis. We now know our value for c is -5.
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Now we simply just substitute our values into the equation. So:
y = mx + c
If m=3/2 and c=-5, then:
y = 3/2x - 5
(Sorry if this was confusing, hope it kinda helped though!)