1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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)

You might be interested in
Given that
BaLLatris [955]

Answer:

x=21/5

Step-by-step explanation:

5x:9 = 7:3

Turn the ratios into fractions:

5x/9 = 7/3

Then cross mutiply

15x=63

x=21/5

8 0
2 years ago
what is the slope and y-intercept? write the equation. this is finally the last problem on my homework
IgorLugansk [536]

(y2-y1)/(x2-x1)

3-2=1

4-2=2

slope: 1/2

y-int: 1

y=1/2x+1

4 0
2 years ago
Read 2 more answers
50 POINTS NEED ANSWER ASAP please! Among these figures, figure blank(A,B,CE), and figure blank(D,E) have the same volume.
Crank

Answer:

Step-by-step explanation:

what is the question?

3 0
3 years ago
Read 2 more answers
1. Kyle is using elimination to solve the system
Andrei [34K]
I think it’s D but I am not sure
7 0
3 years ago
X^2+y^2=25 find the distance of point (x,y) from origin​
storchak [24]

Answer:

5

Step-by-step explanation:

The radius is 5.

All I do was think of the center-radius form a circle

(x-h)^2+(y-k)^2=r^2

x^2     + y^2    =25

(x-0)^2+(y-0)^2=5^2

The center is (0,0) and the radius is 5.

So a point on the circle (x,y) has a distance of 5 from the center

and the center's case here is (0,0).

3 0
2 years ago
Other questions:
  • The farm report this morning said farmers are averaging 56 bushels per acre for their soybean harvest. How many quarts of soybea
    11·1 answer
  • 3 (exponent 9) over 3 (exponent 5) equals? (its a fraction)
    8·1 answer
  • A jar contains 3 black marbles, 4 white marbles and 5 striped marbles. If a marble is picked at random, what is the probability
    7·2 answers
  • The cafeteria manager took a survey of the third grade students and found that 83 of 127 students said they did not want hot dog
    14·2 answers
  • 157 is 16.6% of what number
    9·2 answers
  • Jessica wrote a report
    14·1 answer
  • For the function f(x) = x2 ­ -12, find (f o f­-1)(4)
    12·2 answers
  • Please helpppppppppppppp
    15·1 answer
  • A painter leans a 12-foot ladder against a wall. The angle of elevation of the ladder is 55.
    6·1 answer
  • Find the area of a circle with radius=25cm give your answer rounded to 3sf
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!