Question

Which shows the graph of the solution set of 2x + y < 4?

Answer 1

we have

$2x+y < 4$

Using a graphing tool

see the attached figure

the solution is the shaded area below the line

The answer in the attached figure

Answer 2

Answer and step-by-step explanation:

This inequality can be written similarly to an equation in slope-intercept form, y=mx+b, by isolating the y.  Subtract 2x from each side:

2x+y-2x < 4-2x

y < 4-2x

y < -2x+4

This makes the related equation y = -2x+4.  In this equation, the slope is -2 and the y-intercept is 4.  This means we first plot the point (0, 4) on the y-axis.  The slope is -2, which can be written as -2/1; this means to find the next point, we go from down 2 and right 1 from the y-intercept to plot the next point (1, 2); then down 2 and right 1 for the next point (2, 0).  Since this is strictly less than, and not less than or equal to, we use a dashed line instead of a solid line.

Since this is "less than", this means that we shade the graph under the line.