SOLUTION: Graph the following equations. Calculate the slope, x-intercept and y-intercept, and label the intercepts on the graph. 2x + 3y = 9

Algebra ->  Linear-equations -> SOLUTION: Graph the following equations. Calculate the slope, x-intercept and y-intercept, and label the intercepts on the graph. 2x + 3y = 9       Log On


   

Question 131378: Graph the following equations. Calculate the slope, x-intercept and y-intercept, and label the intercepts on the graph.
2x + 3y = 9
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x%2B3y=9 Start with the given equation


3y=9-2x Subtract 2+x from both sides


3y=-2x%2B9 Rearrange the equation


y=%28-2x%2B9%29%2F%283%29 Divide both sides by 3


y=%28-2%2F3%29x%2B%289%29%2F%283%29 Break up the fraction


y=%28-2%2F3%29x%2B3 Reduce




Looking at y=-%282%2F3%29x%2B3 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=-2%2F3 and the y-intercept is b=3


Since b=3 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




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

Also, because the slope is -2%2F3, this means:

rise%2Frun=-2%2F3


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



So starting at , go down 2 units


and to the right 3 units to get to the next point



Now draw a line through these points to graph y=-%282%2F3%29x%2B3

So this is the graph of y=-%282%2F3%29x%2B3 through the points and


So from the graph, we can see that the x-intercept is and the y-intercept is (0,3)