Step-by-step explanation:
Hello,
First of all, we need to find the equation of the line.
It will be something like y = ax + b (we need to find a and b).
Then the graph is the part of the plan which is above this line, so the inequality will be
There is only one line passing by two different points, right?
We need to find two points of this line, the x-axis gives the x of the point and the y-axis give the y of the point.
We can see on the graph that (-1,-1) and (6,13) are two points of this line.
I attached a graph with the two points A (-1,-1) and B (6,13).
We need to solve y = ax + b to find a and b which means:
(-1) = a(-1 )+ b <=> -1 = -a + b <=> -a + b = -1
(13) = a(6) + b <=> 6a + b = 13
To eliminate b, we can subtract the first equation from the second one.
6a + b -(-a) - b = 13 - (-1) = 13 + 1 = 14
<=> 6a + a = 7a = 14 we can divide by 7 both parts of the equation.
And then, b = -1 + a = -1 + 2 = 1
The equation of the line is then 
So, the inequality is:
And this is the answer of the question 1.
2. First, we find the equation of the line by finding two points on this line. Then, we deduce the inequality from the equality as the graph is all the points above the line (as explained above).
3. A real-life example is the following.
My parents gave $1 to my sister and they will give her $2 every day.
So today at x = 0 she has $1 and her pocket money will be represented by the line. And I told my parents that there were no way I can get less than my little sister. To help them understand what can be an acceptable deal I provided this graph, and I told them to only look for t positive of course.
The label for the x-axis is the time.
The label for the y-axis is the pocket money in $
After one day x = 1 my sister has $3 (point on the line), a possible solution for my pocket money is $6, $14 (two points from the graph) is also a solution of course :-)
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
