When you replace the comparison symbol (<) with an equal sign (=), you get the equation of a line in slope-intercept form:
... y = mx + b
where <em>m</em> is the slope, and <em>b</em> is the y-intercept.
Your equation has m = -1/4 and b = -1. To graph this line, find the point (0, -1) on the y-axis. To find another point on the line, you can use the slope value (rise/run = -1/4), which tells you the line "rises" -1 for each "run" of +4. That is, another point on the line will be 4 units to the right and 1 unit down, at (4, -2). Working in the other direction (to the left, instead of to the right), the -1/4 slope tells you the point 4 units left and 1 unit up (-4, 0) will also be on the line. <em>Draw a dashed line through these points,</em>
The dashed line you just drew is the boundary of the solution region. It is dashed because the line itself is not part of the solution. (Those points do not meet the requirement for "less than.")
Appropriate values of y are ones that are <em>less than</em> those on the line, so the solution region is indicated as being the half-plane <em>below</em> the line. You indicate this by shading the solution region. (See the attachment for an example of the way this can be graphed.)
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If the comparison is ≤ instead of <, then the line is solid (not dashed), indicating it is part of the solution region. If the comparison is > or ≥, then the shaded region is <em>above</em> the line, where y-values are greater than those on the line.
