Question

What is the equation of the line that passes through the points four over 5 , and one over five and then one half , and three over two

Answer 1

Your answer is y = -(13/3)x + 11/3. I have put the brackets to show that the entire fraction is negative, they do not do anything else.
First we need to find the slope of the line using the equation (y2 - y1)/(x2 - x1), so we get (3/2 - 1/5)/(1/2 - 4/5). To make this easier, I did each subtraction separately:
3/2 - 1/5 = 15/10 - 2/10 = 13/10
1/2 - 4/5 = 5/10 - 8/10 = -(3/10)
And then we need to divide 13/10 by -(3/10), so:
13/10 ÷ -(3/10) = 13/10 × -(10/3) = -(130/30) = -(13/3), which is our slope.
Then, we can write the equation y = -(13/3)x + c, and substitute in coordinates:
3/2 = (-13/3 × 1/2) + c
3/2 = -(13/6) + c
c = 11/3
So the final equation is y = -(13/3)x + 11/3.
I hope this helps!