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Which linear inequality is represented by the graph?y ≤ x − 1y ≥ x − 1y < 3x − 1y > 3x − 1

Which linear inequality is represented by the graphy x 1y x 1y lt 3x 1y gt 3x 1 class=

Respuesta :

merlynthewhizz
First, work out the equation of the graph.
Equation of a straight line graph is given in the form [tex]y = mx+c[/tex] where [tex]m[/tex] is the slope of the line and [tex]c[/tex] is the y-intercept.

The graph given shows the line intercept y-axis at (0, -1)

To work out the slope, choose any two coordinates then find their vertical and horizontal distance. Say we choose (0, -1) and (3, 0)
The vertical distance is 1 and the horizontal distance is 3, so the slope is
[tex]m = \frac{-1-0}{0-3}= \frac{-1}{-3}= \frac{1}{3} [/tex] 

Then form the equation for the line
[tex]y=mx+c[/tex]
[tex]y= \frac{1}{3}x-1 [/tex]→ Multiply each term by 3
[tex]3y = x - 3[/tex]

Now the inequality part, the shaded region is above the line, so the values intended are 'greater than' and the line is a bold line, so the inequality is 'greater than or equal to' and the symbol is ≥

The inequality is then
3y ≥ x - 3

Note: None of the options show this answer. Maybe check if the original options have been copied correctly. 

Solution: As the line shown in the graph passes through (3,0) and (0,-1).

So, equation of line passing through (3,0) and (0,-1) is given by two point formula i.e equation of line passing through (p,q) and (a,b) is given by

→[tex]\frac{y-q}{x-p}=\frac{q-b}{p-a}[/tex]

→[tex]\frac{y-0}{x-3}=\frac{0+1}{3-0}[/tex]

So ,the equation of line is ,→3 y = x-3

  → x- 3 y -3= 0 or y=x/3 -1

take point (0,0) and putting in the above equation, we see that ,L.H.S>R.H.S

Similarly if you take other points , like (1,0).(0,1) we see that ,L.H.S>R.H.S.

it means the above equation can be written as , y≥x/3 -1.

None of the option is correct.