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Answer :

Answer:

3x-2y=10

2y=3x-10

Y=(3/2)x-5

Slope m=3/2

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Answer:

See attachment.

Step-by-step explanation:

Slope-intercept form:

[tex]\boxed{y=mx+b}[/tex]

where:

  • m = slope
  • b = y-intercept

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Given inequality:

[tex]3x-2y < 10[/tex]

Rearrange the given inequality to make y the subject:

[tex]\implies 3x-2y+2y < 10+2y[/tex]

[tex]\implies 3x < 10+2y[/tex]

[tex]\implies 3x-10 < 10+2y-10[/tex]

[tex]\implies 3x-10 < 2y[/tex]

[tex]\implies 2y > 3x-10[/tex]

[tex]\implies \dfrac{2y}{2} > \dfrac{3}{2}x-\dfrac{10}{2}[/tex]

[tex]\implies y > \dfrac{3}{2}x-5[/tex]

Compare this with the slope-intercept form.  

Therefore:

  • slope = ³/₂
  • y-intercept = (0, -5)

When graphing inequalities:

  • < or > : dashed line.
  • ≤ or ≥ : solid line.
  • < or ≤ : shade under the line.
  • > or ≥ : shade above the line.

To graph the given inequality using its slope and y-intercept:

  • Plot the y-intercept → point (0, -5).  
  • As the slope is ³/₂, plot another point 3 units up and 2 units right from (0, -5)  → point (2, -2).  
  • Draw a dashed straight line through the two points.
  • Shade above the line.

Learn more about graphing inequalities here:

https://brainly.com/question/27743925

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