Which description of the graph of the linear inequality y ≥ 7x – 4 is correct? 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.

      Correct description of the given inequality will be, A solid line with y-intercept (-4) and slope 7. The graph will be shaded above the line.

 Slope form of the line is given by equation,

y = mx + b

Where 'm' = Slope of the line

b = y-intercept

For a line having equation,

y = 7x - 4

Slope = 7

y-intercept = -4

If the line is an inequality, properties of the inequality will be defined by,

• If the line is having a sign equal to (=), graph of the line will be a solid line.
• If the solid line has a sign of greater than (>), solution set (shaded region) of the inequality will be above the line.
• If the line has a sign of less than (<), solution set of the inequality will be below the line.

By these properties,

inequality y ≥ 7x - 4 will show,

• A solid line with slope 7 and y-intercept as (-4).
• Shaded area will be above the solid line.

  Therefore, the graph will be a solid line with y-intercept (-4) and slope 7. The graph will be shaded above the line.

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Answer:

The correct option is B

B) 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.

Step-by-step explanation:

The given equation is

y ≥ 7x - 4

Consider only the equality sign:

y = 7x-4

or

y = 7x + (-4)

The general form of any linear equation is given by:

y = mx + c

By comparing, we can see that:

m = slope = 7

Secondly consider the equation

y ≥ 7x - 4

We know that generally for the signs "equal to and greater/smaller than", we use a solid line, and for the signs "greater/smaller than", we use a dashed line.

Hence, to graph this equation we'll use a solid line.

Thirdly, find y intercept by putting x=0

y = 7(0) - 4

y = -4

The correct option is B