Question

does anyone know how to solve this? i dont remember doing any problems in class related to this and this single question alone has been stressing me out

Answer 1

• y ≥ x +9
• y > -4x -10

Explanation:

If you have graphed linear equations and inequalities, working this should not be stressful. You are working backward from the graph to determine what the equation must be.

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For the solid line, the y-intercept is +9 (where it crosses the y-axis) and the slope is 1 unit of rise for each 1 unit of run. The slope-intercept form of the equation is then ...

y = x + 9

Since the line is solid and the shading is above it, the associated inequality is ...

y ≥ x + 9

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For the dashed line, the y-intercept is -10. The line has a "rise" of -4 for each 1 unit of run, so its slope is -4. The slope-intercept form of the equation is then ...

y = -4x -10

Since the line is dashed (does not include the "or equal to" case), and shading is above it, the associated inequality is ...

y > -4x -10

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In summary, the system of inequalities is ...

• y ≥ x +9
• y > -4x -10

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If shading is below, then the relation symbol is < or ≤.

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You know that slope-intercept form of the equation of a line is ...

y = mx + b . . . . . . where m is the slope and b is the y-intercept

Answer 2

The answer to your question is below

Explanation:

Process

1.- Get two points of each line to find the equation of each line

Continuous line A (-10, 0) B (0, 9)

Dotted line C (-2, -3) D (0, -10)

Slope continuous line m =
`(9 - 0)/(0 + 10) = = (9)/(10)`

Slope dotted line m =
`(-10 + 3)/(0 + 2) = (-7)/(2)`

2.- Get the equation of each line

Continuous line y + 0 = 9/10 (x + 10)

y = 9/10x + 9

Dotted line y + 3 = -7/2(x + 2)

y + 3 = -7/2x - 7

y = -7/2x -7 - 3

y = -7/2x - 10

3.- Find the inequalities

Continuous line (we need the upper area of the line, we use ≥)

y ≥ 9/10x + 9

The Dotted line (we also need the upper area, we use >)

y > -7/2x - 10