Hi I need to write these systems of equalities in slope intercept form so I can graph them. 20x+4.5y<=60 and 12x+20y<=60.
y=4 4/9x+ 13 1/3 (I think this is wrong)
y=-3/5x+3
Does your teacher insist that you have the relations in slope y-intercept form?
I will show you an easy way to sketch a graph if they are written in the form
ax + by = c
e.g. your 12x + 20y ≤ 60 or the boundary 12x + 20y = 60
put your pinkie finger over the x term (you let x=0)
what you see is 20y = 60
so in your head , y = 3 ---> the point (0,3), the x-intercept
now put your pinkie finger over the y term (you let y = 0)
what you see is 12x=60
so in your head , x = 5 ---> the point (5,0)
so now you have 2 simple points to graph your boundary.
do the same thing for the first one,
you might want to use your calculator for
4.5y = 60
y = 13 1/3
btw, your equations in the slope y-intercept form should have been
y ≤ - (4 4/9)x + 13 1/3
last one is right
To write the given systems of inequalities in slope-intercept form, we need to rearrange the equations so that the variable "y" is isolated on the left side.
First, let's work on the first equation: 20x + 4.5y ≤ 60.
Step 1: Subtract 20x from both sides:
4.5y ≤ -20x + 60.
Step 2: Divide both sides by 4.5 to isolate "y":
y ≤ (-20/4.5)x + (60/4.5).
Simplifying further:
y ≤ -40/9x + 40/3.
So, the first equation can be written as y ≤ (-40/9)x + 40/3.
Next, let's work on the second equation: 12x + 20y ≤ 60.
Step 1: Subtract 12x from both sides:
20y ≤ -12x + 60.
Step 2: Divide both sides by 20 to isolate "y":
y ≤ (-12/20)x + (60/20).
Simplifying further:
y ≤ (-3/5)x + 3.
So, the second equation can be written as y ≤ (-3/5)x + 3.
Regarding the equation y = 4 4/9x + 13 1/3, it seems that there might be an error. The equation should have a "y =" at the beginning, but it appears as if it is missing. Additionally, the fraction format should be standardized. Once the equation is correctly written, it can be considered in slope-intercept form.
Finally, the equation y = -3/5x + 3 is already in slope-intercept form, where the slope is -3/5 and the y-intercept is 3.
Once the equations are in slope-intercept form, you can easily graph them by plotting the y-intercept on the y-axis and using the slope to find other points to plot.