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vfiekz [6]
3 years ago
15

which equation is the point-slope equation of the line that passes through the points (-2,-1) and (7,-4)?

Mathematics
1 answer:
zvonat [6]3 years ago
6 0

Answer:

B (for question 7)

Step-by-step explanation:

To find the slope, we use the equation m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }.

m = (-4+1)/(7+2) = -3/9 = -1/3

Since B is the only option that would give a slope of -1/3, B must be the answer.

(you can use this same method for question 8)

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7. Find the slope-intercept form of the equation of the line that passes through
KATRIN_1 [288]

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y=-2x+2

Step-by-step explanation:

If you bring the 4x to the other side by subtracting it, you will have 2y=-4x+8

then divide by the 2 to get y=-2x=4

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7 0
3 years ago
Find the distance from point A(−9,−3) to the line y = x−6. Round your answer to the nearest tenth.
Vladimir79 [104]

The distance from point A(−9,−3) to the line y = x−6 is 8.5 units

<u>What is slope ?</u>

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

step 1

Find the slope of the perpendicular line to the given line

y=x-6 ---> given line

The slope is m=1

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

m1*m2 = -1

we have

m1=1

substitute

(1)*m2 = -1

so

m2 = -1

step 2

Find the equation of the perpendicular line to the given line

The equation in point slope form is

y-y1=m(x-x1)

we have

m=-1

(x1,y1)=(−9,−3)

substitute

y+3=-1(x+9)--> equation in point slope form

y+3= -x-9

y= -x-12---> equation in slope intercept form

step 3

Find the intersection point between the given line and the perpendicular line to the given line

we have the system of equations

y = x−6.

y= -x-12

Solve the system by graphing

The intersection point is (-3,-9)

see the attached figure

step 4

we know that

The distance between the point A and the point (-3,-9) is the same that the distance between point A and the line y=x-6

the formula to calculate the distance between two points is equal to

d=√[(y2-y1)² + (x2-x1)²]

substitute the values

d=√[(-9+3)² + (-3+9)²]

d= √72 units

simplify

d= 6√2 = 8.5 units

To learn more about the slope from the given link

brainly.com/question/16949303

#SPJ1

8 0
1 year ago
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