SOLUTION: find the gradient of the line 2y - 3x = 5, and draw the line on a graph paper

Algebra ->  Linear-equations -> SOLUTION: find the gradient of the line 2y - 3x = 5, and draw the line on a graph paper      Log On


   

Question 161943: find the gradient of the line 2y - 3x = 5, and draw the line on a graph paper
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2y-3x=5 Start with the given equation.


2y=5%2B3x Add 3x to both sides.


2y=3x%2B5 Rearrange the terms.


y=%283x%2B5%29%2F%282%29 Divide both sides by 2 to isolate y.


y=%283%2F2%29x%2B%285%29%2F%282%29 Break up the fraction.


y=%283%2F2%29x%2B5%2F2 Reduce.


So the equation y=%283%2F2%29x%2B5%2F2 is now in slope intercept form y=mx%2Bb where the slope (ie gradient) is m=3%2F2 and the y-intercept is b=5%2F2




Since b=5%2F2 this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis

So we have one point which is (0,2.5)




Now since the slope is comprised of the "rise" over the "run" this means
slope=rise%2Frun

Also, because the slope is 3%2F2, this means:

rise%2Frun=3%2F2


which shows us that the rise is 3 and the run is 2. This means that to go from point to point, we can go up 3 and over 2



So starting at , go up 3 units


and to the right 2 units to get to the next point



Now draw a line through these points to graph y=%283%2F2%29x%2B5%2F2

So this is the graph of y=%283%2F2%29x%2B5%2F2 through the points and