Question

this graph shows the solution to which inequality (3 3) (-3 -1)

Answer 1

Answer:

B

Step-by-step explanation:

since the graph shows dotted line the sign has to be < or > so C and D eliminated from your answer

y>2/3 x +1 is your answer (B)

Answer 2

Answer:

$\boxed{y > \frac{2}{3} x + 1}$

Option B is the correct option.

Step-by-step explanation:

point ₁ ( - 3 , - 1 ) x₁ = - 3 , y₂ = - 1

point ₂ ( 3 , 3 ). x₂ = 3 , y₂= 3

Now, let's find the slope:

Slope ( m ) = $= \frac{y2 - y1}{x2 - x1}$

$= \frac{3 - ( - 1)}{3 - ( - 3)}$

$= \frac{3 + 1}{3 + 3}$

$= \frac{4}{6}$

$= \frac{2}{3}$

At ( 3 , - 1 )

y = mx + c , where m is the gradient / slope amd c is called the intercept on y-axis

$- 1 = \frac{2}{3} \times ( - 3) + c$

Solve for c

$- 1 + 2 = c$

$c = 1$

Since, The red line is dotted line. Therefore it does not include the equal to part. And the shaded region is upper part. Hence, ' > ' should be used.

The answer would be:

$y > \frac{2}{3} x + 1$

Hope I helped!

Best regards!