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Deffense [45]
3 years ago
5

Which system of inequalities has a line as a solution?

Mathematics
1 answer:
erastova [34]3 years ago
7 0

linear inequality

The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system

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Determine the equation of each line with the following properties:
iris [78.8K]

Answer:

a) y =2/3 x + 7.

b) x = -1

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d) y = -3/2 x + 5/2.

Step-by-step explanation:

a) Intercept form y = mx + b where m = 2/3 and  b = 7

b) y can take any value but x is always -1.

c) Slope m = (-1-3)/ (1 - -4)

= -4/5

Using point-slope form where m = -4/5 and x1 y1 = 1 , -1:

y - y1 = m(x - x1)

y - -1 = -4/5(x - 1)

y + 1 = -4/5x + 4/5

y = -4/5 x - 1/5

d)  The slope m of the line perpendicular to this line is:

-1 / 2/3

m = -3/2.

When x = -1 , y = 4 so using the slope intercept form of a line

y = mx + b

4 = -3/2 * -1 + b  where b = the y-intercept.

4 = 3/2 + b

b = 4 - 3/2 = 5/2.

The equation is  y = -3/2 x + 5/2.

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