Question

Change to slope-intercept form. Then find the y-intercept, first point, and second point.

Answer 1

Answer:

1) $y> \frac{x}{3}+2$ 2) (0,2) 3) The first and second Points must have x coordinate <-6, or y-coordinate  y >2 e.g. (-7,2), (-6,3)

Step-by-step explanation:

1) To Rewrite it as Slope-intercept form, is to isolate the y on the left side and on the right side the rest of the inequality.

$-x+3y>6\Rightarrow 3y>x+6 \Rightarrow y> \frac{x+6}{3}\Rightarrow y> \frac{x}{3}+2$

2) Since this is a linear inequality the y intercept is given by "b" parameter.$y> mx+b \Rightarrow y> \frac{x}{3}+2 \Rightarrow b=2$

So the y-intercept is y > 2, coordinate point (0,2). In the graph, we have a dashed line over 2.

3) Since there no choices, the points that satisfy this inequality lie within the green area. We know that the points for this inequality must satisfy  x < -6 or y> 2:

Testing for (-7,2)  for x<-6 ⇒-7 <-6

$-x+3*y>6\\-(-7)+3*2>6\\7+6>6\\13>6\:\\True$

Testing for (-6,3)  for y>2 ⇒3>2

$-x+3*y>6\\-(-6)+3*3>6\\6+9>6\\15>6\:True$