What is an equation of the line that passes through the points (6,4) and (4,1)? Put your answer in fully reduced form.

y = 3/2x - 5

Step-by-step explanation:

The equation for a linear line is y=mx+c:

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!)