Question

Y=6/5x+9 how would I graph it

Answer 1

To graph this linear function, we can find both intercepts of the function. To achieve this, we need to solve the equation when y = 0 (for this function) (this will be the x-intercept), and then we need to solve the resulting equation for this function when x = 0 (this will be the y-intercept). Then, we will have two points for which we can graph the function - we need to remember that a line is defined by two points.

Then, we can proceed as follows:

1. Finding the x-intercept

`y=(6)/(5)x+9,y=0\Rightarrow0=(6)/(5)x+9`

Then, we have:

a. Add -9 to both sides of the equation:

`(6)/(5)x=-9`

b. Multiply both sides of the equation by 5/6:

`(5)/(6)(6)/(5)x=-9\cdot(5)/(6)\Rightarrow x=-(45)/(6)=-(15)/(2)=-7.5`

Therefore, the x-intercept is (-7.5, 0).

2. Finding the y-intercept

We have that x = 0 in this case. Then, we have:

`y=(6)/(5)x+9\Rightarrow y=(6)/(5)(0)+9\Rightarrow y=9`

Therefore, the y-intercept is (0, 9).

Now, we have the points (-7.5, 0) and (0, 9), and we can draw both points on the coordinate plane. The line will pass through these two points: