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anzhelika [568]
3 years ago
13

Consider the graph of the line y = x – 4 and the point (−4, 2).

Mathematics
1 answer:
Hitman42 [59]3 years ago
8 0

Answer:

a. The slope  of a line parallel to the given line is 1

b. A point on the line parallel to the given line, passing through (−4, 2), is  (1,7)

c. The slope of the line perpendicular to the given line is -1

d. A point on the line perpendicular to the given line, passing through (−4, 2), is (3,-5)

Step-by-step explanation:

The equation of the line in Slope-intercept form  is:

y=mx+b

Where m is the slope and b is the y-intercept.

a. For the line y = x - 4

You can identify that:

m=1

 By definition, two lines are parallel if they have the same slope. Then, the  slope of a line parallel to the given line is:

m=1

b. The equation of the line in Point-slope form is:

y -y_1 = m(x - x_1)

Where m is the slope and (x_1,y_1)  is a point of the line.

Given the point (-4,2), substitute this point and the slope of the line into the equation:

 y -2 = (x +4)

Give a value to "x", substitute it into this equation and solve for "y":

For x=1 :

y -2 = (1 +4)

y= 5+2

y= 7

Then, you get the point (1,7)

c. The slopes of perpendicular lines are negative reciprocals, then the  slope of a line perpendicular to the given line is:

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

d. Given the point (-4,2), substitute this point and the slope of the line into the equation:

 y -2 = -1(x +4)

 y -2 = -(x +4)

Give a value to "x", substitute it into this equation and solve for "y":

For x=3 :

y -2 = -(3 +4)

y= -7+2

y= -5

Then, you get the point (3,-5)

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(15.5)/(12.4) = 1.25

So the larger figure on the right has side lengths that are 1.25 times larger compared to the corresponding sides of the figure on the left.

You'll need to flip the figure on the left so that the side labeled "20" is along the top, and the "28" is along the bottom.

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Because we have similar proportions as discussed earlier, and congruent pairs of angles like this, this shows the two figures are similar quadrilaterals. The one on the right is simply an enlarged scaled up copy of the figure on the left.

3 0
2 years ago
4a-b<br> Evaluate the expression when a=5 and b=-7
stepladder [879]

Answer:

27

Step-by-step explanation:

So first we need to plug in 5 as the variable a and -7 as the variable b

4(5)-(-7)

Next we multiply the 4 and the 5 together to get 20

4(5) = 20   or    4 x 5 = 20

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This can also be written as 20 plus 7 as a mathematical rule states: two negatives make a positive. So:

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Both of these are equivalent in every sense of the word and give us our final answer of 27

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lapo4ka [179]

Answer:

= 5

Step-by-step explanation:

(2/100) × (250/1)

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3 years ago
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vfiekz [6]

Answer:

none of the answers listed are equivalent to b (22/5, 11/8, 2/5, 1/4)

Step-by-step explanation:

\frac{1}{3b} = \frac{4}{5}

to simplify, cross multiply

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divide both sides by 12 to isolate b,

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\frac{5}{12} = b

None of the answers listed are equivalent to 5/12

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\frac{5}{12} \neq\frac{11}{8}

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\frac{5}{12} \neq\frac{1}{4}

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8
You can divide it to 6 square and a triangle
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