Answer:
3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679
To change it into slope intercept (y=mx+b) you just replace the inequality with an equality and isolate y
x<=2:
x=2=y-> y=2 or y=2+0x
2x-3y>=4:
2x-3y=4
2x-4=3y
(2/3)x-(4/3))=y
y=(2/3)x-(4/3)
x+y>0:
x+y=0
y=-x or y=-x+0
So just plug in the numbers (x,y) into the equations.
A) (7.5, -5)
2(7.5) -5 = 10
15 - 5 = 10 yup, this works.
Let's see if it works for other equation.
-2(7.5) + 2(-5) = 5
-15 - 10 = 5 nope, this does not work.
B) (-2.5, -5)
2(-2.5) - 5 = 10
-5 - 5 = 10 nope, doesn't work
Since it doesn't work we don't need to try for other equation.
C) (2.5, 5)
2(2.5) + 5 = 10
5 + 5 = 10 yup, this works.
Now the other equation.
-2(2.5) + 2(5) = 5
-5 + 10 = 5 and this works.
So the solution to this set is answer choice C
Step 1: Find the gradient/slope
Gradient and slope are interchangeable words. To find the gradient/slope we need to use two points that we know are on the line and the following formula: (y2 - y1) / (x2 - x1)
Point 1 = (0,1)
Point 2 = (3,13)
Gradient = (13 - 1) / (3 - 0)
Gradient = 12 / 3
Gradient = 4
Step 2: Find the y-intercept
We can use the slope-intercept form to find the y-intercept. To do so, we plug in the gradient and one of the points on the line. You can pick either point to plug in here!
Slope-intercept form: y = mx + b
-m is the gradient
-b is the y-intercept (that we are trying to find)
13 = 4(3) + b
13 = 12 + b
b = 1
Step 3: Put it all together in slope-intercept form
Now that we have the slope and y-intercept, all that's left to do is plug in the values.
y = mx + b
y = 4x + 1
Answer: y = 4x + 1
Hope this helps!!