Question

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.

Answer 1

Answer:

The given inequality is y ≥ 7x - 4

Now, considering the equality sign alone

y = 7x - 4

y = 7x + (-4) --- (1)

The general form of any linear equation in slope-intercept form is given by

y = mx + c --- (2)

By comparing (1) and (2)

mx = 7x

m = 7

Next, 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.

So, to graph this we use a solid line.

Now, find the y-intercept.

Put x = 0

y = 7(0) - 4

y = -4

Therefore, 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.