Answer:
The graph of inequality [tex]5x+2y\geq 13[/tex] is above the solid line.
Step-by-step explanation:
Step-by-step explanation:
An inequality on a coordinate plane consist of a boundary line and an area in which each point is a possible solution.
* If the inequality has a sign or , then the line will be a solid line and its point are included in the solution.
* If the inequality has a sign '>' or '<' , then the line will be a dotted line and its point are not included in the solution.
Given: The linear inequality: [tex]5x+2y\geq 13[/tex]
Then, the equation of the boundary line is; 5x+2y =13 ......[1]
we can write this as;
[tex]2y = -5x+13[/tex]
Divide by 2 we get;
[tex]y = -\frac{5}{2} x + \frac{13}{2}[/tex] ......[2]
Compare this boundary line equation with the general point slope intercept line i.e, y = mx+b where m is the slope and b is the y-intercept.
Therefore, the slope of the this line is, m =[tex]-\frac{5}{2}[/tex]
and a y-intercept (b) = [tex]\frac{13}{2}[/tex] = 6.5
To find x -intercept:
Substitute y =0 in to solve for x;
[tex]5x+0 =13[/tex]
Simplify:
[tex]x =\frac{13}{5} = 2.6[/tex]
Therefore, the x-intercept is 2.6
Now,
Plot [tex]y = -\frac{5}{2} x + \frac{13}{2}[/tex] ( as a solid line because [tex]y\geq[/tex] included equal to)
and shade the area above as [tex]5x+2y\geq 13[/tex] as shown below in the graph
