# What is the equation ?

What is the equation based on the graph below. Relevance
• Two points on dashed line: (0, -3) and (2, 7).

Slope of dashed line = (7 - (-3)) / (2 - 0) = 10 / 2 = 5

Y-intercept: (0, -3)

y = mx + b

y = 5x - 3 is equation of dashed line.

Trying (0, 0), in the shaded region, gives 0 > -3

So, the shaded region is represented by y > 5x - 3.

• Let's start with the line.  We want something in the form of:

y = mx + b

The x-intercept is (0, -3), so b = -3:

y = mx - 3

Now we look at the slope.  I think of it as "rise over run".  So starting with (0, -3), find the next point on the line where we can find it on the grid.  I see point (1, 2).  The "rise" is 5 and the "run" is 1, so the slope is:

m = 5/1

m = 5

Now the equation is:

y = 5x - 3

Now we need to look at it as an inequality.  You want to see if the shaded region is above the line (>) or below the line (<)

The shaded region is above the line, so the inequality is now:

y > 5x - 3

Finally, we look at if the line is solid or dashed.  If it's solid, the solution includes the points on the line (≥) and if dashed the line does not include solution data points (>).  It is dashed, so the solution is:

y > 5x - 3