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Digiron [165]
3 years ago
15

What is the equation of the line that passes through points (-3, 0.5) and (3, -0.5)

Mathematics
1 answer:
marissa [1.9K]3 years ago
7 0

Answer:

y = (-1/6)x

Step-by-step explanation:

As we move from  (-3, 0.5) to (3, -0.5), x increases by 6 and y decreases by 1.

Hence, the slope of this line is m = rise / run = -1/6.

Starting with the slope-intercept form of the equation of a straight line, we have:

y = mx + b.  We substitute 0.5 for y, -3 for x and -1/6 for m, obtaining:

0.5 = (-1/6)(-3) - b, or:

0.5 = 0.5 - b.  Then b = 0, and the desired equation is

y = (-1/6)x

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ABCD is a parallelogram. Determine the length of AD. ANSWERS: A) 2.5 units B) 10 units C) 11 units D) 5 units
noname [10]

Answer:

D) 5

Step-by-step explanation:

Since 2x = x+5, we have x = 5.

6 0
3 years ago
Function 1: y = 4x + 5
evablogger [386]
Answer: function 1

Rate of change of function 1:
Following the format of y=mx+c, the rate of change should be m, so, the rate of change for function 1 = 4

To find the gradient (rate of change):
The two points the line passes through are (x1, y1) and (x2, y2), which in this case is (1, 6) and (3, 10)
(Doesn't matter which is which but you need to make sure that once you decide which is which, you stick to it)
To calculate the gradient, you substitute these values following (y1 - y2)/(x1 - x2)

Gradient of function 2 = (10 - 6)/(3 - 1)
= 2

Therefore, since 4 > 2, rate of change of function 1 > rate of change of function 2.
6 0
3 years ago
Which system of inequalities does the graph represent? Which test point satisfies both of the inequalities in that system?
AveGali [126]

Answer:

1) The inequality for the given system are

y ≥ 4x - 4

y ≥ x - 1.5

2)  The test point (0,0)  satisfies both of the inequalities in the system represented by the graph.

Step-by-step explanation:

Given : A graph showing  a system of inequalities.

We have to find the system of inequality.

For line 1)

The points that cut the x and y axis are (1,0) and (0,-4)

Thus, we can find the equation of line using two given point.

Since the general equation of line is y = mx + c

Where m is slope and c is y intercept

Slope is find as m=\frac{y_2-y_1}{x_2-x_1}

Substitute, we get,

m=\frac{-4-0}{0-1}=4

Slope is 4.

Thus, equation becomes y = 4x + c

For c put (0,-4)  in the above equation , we have,

-4 = 4(0) + c ⇒ c = -4

Thus, equation becomes y = 4x - 4

For inequality take a test point (0,0) and we check for which inequality it satisfies the graph region

For (0,0)

y = 4x - 4 becomes 0 = - 4  is satisfied when 0 > -4

thus, the inequality becomes y ≥ 4x - 4

Since, the line is a solid so it will take up equality sign too.

For line 2)

The points that cut the x and y axis are (1.5,0) and (0,-1.5)

Thus, we can find the equation of line using two given point.

Since the general equation of line is y = mx + c

Where m is slope and c is y intercept

Slope is find as m=\frac{y_2-y_1}{x_2-x_1}

Substitute, we get,

m=\frac{-1.5-0}{0-1.5}=1

Slope is 1.

Thus, equation becomes y = x + c

For c put (0,-1.5)  in the above equation , we have,

-1.5 = (0) + c ⇒ c = - 1.5

Thus, equation becomes y = x - 1.5

For inequality take a test point (0,0) and we check for which inequality it satisfies the graph region

For (0,0)

y = x - 1.5 becomes 0 = -1.5  is satisfied when 0 > - 1.5

thus, the inequality becomes y ≥ x - 1.5

Since, the line is a solid so it will take up equality sign too.

Thus, the inequality for the given system are

y ≥ 4x - 4

y ≥ x - 1.5

Also,  The test point (0,0)  satisfies both of the inequalities in the system represented by the graph.

6 0
3 years ago
Bill spent 50% of his savings on school supplies, then he spent 50% of what was left on lunch. If he had $6 left after lunch, ho
Lera25 [3.4K]

If he spent half his savings on supplies and the other half on lunch he shouldn't have money left over. It's a trick question.

6 0
3 years ago
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Which of the equations is proportional if y is a function of X?
Taya2010 [7]

Answer:

y=4x

Step-by-step explanation:

it goes through 0,0 on my graph

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