Question

Write an inequality, in slope-intercept form, for the graph below. If necessary,use "<=" for < or ">" for >(4,2)(-4,0)

Answer 1

EXPLANATION

We can write an inequality in slope-intercept form by using the two given points, (x_1,y_1)= (-4,0) and (x_2,y_2)=(4,2), as shown as follows:

`\text{Slope}=((y_2-y_1))/((x_2-x_1))`

Replacing terms:

`\text{Slope}=((2-0))/((4-(-4)))`

Subtracting terms:

`\text{Slope}=(2)/(8)=(1)/(4)`

Now, we need to find the y-intercept.

As we can see in the dashed line, the y-intercept is at point (x,y)=(0,1).

Hence, the equation of the dashed line is as follows:

y = (1/4)x + 1

But as the solution represents all the points that are below this line, the inequality should be as following:

y < (1/4)x + 1