Answer:
y < 2/3 x - 1 is the linear inequality which represented by the graph ⇒ 4th answer
Step-by-step explanation:
* Lets explain how to solve the problem
- At first lets find the equation of the line
∵ The line passes through points (3 , 1) and (-3 , -3)
∵ The form of the equation is y = mx + c, where m is the slope of the
line and c is the y-intercept
- The rule of the slope of any line passes through points (x1 , y1) and
(x2 , y2) is m = (y2 - y1)/(x2 - x1)
- The y-intercept means the intersection between the line and the
y-axis at point (0 , c)
∵ (3 , 1) and (-3 , -3) are two points on the line
- Let (x1 , y1) is (3 , 1) and (x2 , y2) is (-3 , -3)
∴ The slope of the line m = (-3 - 1)/(-3 - 3) = -4/-6 = 2/3
∵ The line intersects the y-axis at point (0 , -1)
∴ c = -1
∵ The equation of the line is y = mx + c
∴ The equation of the line is y = 2/3 x + -1
∴ The equation of the line is y = 2/3 x - 1
- If the shaded part is over the line then the sign of inequality is ≥ or >
- If the shaded part is under the line then the sign of inequality is ≤ or <
- If the line represented by solid line (not dashed), then the sign of
inequality is ≥ or ≤
- If the line represented by dashed line (not solid), then the sign of
inequality is > or <
∵ The shading part is under the line
∵ The line is dashed
∴ The sign of the inequality is <
∴ y < 2/3 x - 1
* y < 2/3 x - 1 is the linear inequality which represented by the graph
