Question

which description of the graph of the linear equality y ≥ 7x – 4 is correct? please help the graph will be a dashed line with a y-intercept of negative four and a slope of seven. the graph will be shaded below the line. the graph will be a solid line with a y-intercept of negative four and a slope of seven. the graph will be shaded above the line. the graph will be a solid line with a y-intercept of seven and a slope of negative four. the graph will be shaded below the line. the graph will be a dashed line with a y-intercept of seven and a slope of negative four. the graph will be shaded above the line.

Answer 1

graph will be a solid line (because of the equal sign). with a y int of -4 and a slope of 7, and it will be shaded above the line (because it is greater)

Answer 2

The graph will be a solid line with a y-intercept of negative four and a slope of seven. The graph will be shaded above the line.

Explanation:

In IR2 we can write any line in this form :

`y=ax+b`

Where ''a'' is the slope and when
`x=0` ⇒

`y=(a).(0)+b\\y=b` ⇒
`(0,b)` is the point in which the line intersects the y-axis and ''b'' is the y-intercept.

To solve the linear equality
`y\geq7x-4` we must first work with the expression
`y=7x-4`

This line has a slope of 7 given that 7 is multiplying the variable x and a y-intercept of - 4

This line will divide the plane into two regions :

The region above the line and the region below the line

To decide which region we need to shade, we can put any arbitrary point in the expression
`y\geq 7x-4` and see what happen.

For example the point
`(0,0)` ⇒

`y\geq 7x-4\\0\geq (7).(0) - 4\\0\geq -4`

This final expression is true, therefore the point
`(0,0)` belongs to the region
`y\geq 7x-4` and we conclude that we need to shade above the line.

Given that in the expression
`y\geq 7x-4` we have the symbol
`\geq` and not > , we must include the line in the region. The line will be a solid line.

The correct description is '' The graph will be a solid line with a y-intercept of negative four and a slope of seven. The graph will be shaded above the line ''

I add a graph of the linear equality.