The point at which two lines meet is referred to as the point of intersection.
- The point of intersection with the y-axis is: [tex](0,13)[/tex].
- The point of intersection with the x-axis is: [tex](13,0)[/tex].
- The area of the triangle is 84.5 square units
The linear equation is given as:
[tex]y = 13 - x[/tex]
Intersection with the y-axis
Set [tex]x=0[/tex],
[tex]y = 13 - x[/tex]
[tex]y = 13 - 0[/tex]
[tex]y = 13[/tex]
This means that: [tex]y = 13 - x[/tex] intersects with the y-axis at: [tex](0,13)[/tex]
Intersection with the x-axis
Set [tex]y=0[/tex],
[tex]y = 13 - x[/tex]
[tex]0 = 13 - x[/tex]
[tex]x = 13[/tex]
This means that: [tex]y = 13 - x[/tex] intersects with the x-axis at: [tex](13,0)[/tex]
The area of the right-angled triangle
The area is calculated as:
[tex]Area = 0.5 \times Base \times Height[/tex]
In this case,
[tex]Base = x[/tex]
[tex]Height = y[/tex]
So, we have:
[tex]Area = 0.5 \times x \times y[/tex]
This gives:
[tex]Area = 0.5 \times 13 \times 13[/tex]
[tex]Area = 84.5[/tex]
Hence, the area of the triangle is 84.5 square units
See attachment for the graph of
[tex]y = 13 - x[/tex]
Read more about graphs at:
https://brainly.com/question/11897796
