PRACTICE QUESTIONS ON FINDING EQUATIONS OF LINE WITH POINT AND SLOPE

Find the equation of the line from the given point and slope

Solution

13. The graph of the a line in the xy-plane has slope 2 and contains the point (1, 8). The graph of a second line passes through the points (1, 2) and (2, 1). If the two lines intersect at the point (a, b) what is the value of a + b ?

a)  4    b)  3    c)  -1   d) -4

Solution

Write the equation of the line in standard form 

Problem 1 :

Write the following linear equation in standard form.

y  =  3x + 1

Solution

Problem 2 :

Write the following linear equation in standard form.

y  =  x/2 - 3

Solution

Problem 3 :

Write the following linear equation in standard form.

y  =  1/4 - 7x/2

Solution

Problem 4 :

Write the following linear equation in standard form.

y  =  -5x/4 + 1/6

Solution

Problem 5 :

The line y = kx + 4, where k is a constant is graphed in the xy-plane. If the line contains the point (c, d) where c ≠ 0 and d ≠ 0, what is the slope of the line in terms of c and d ?

a)  (d - 4) / c     b)  (c - 4) / d      c) (4 - d) / c

d)  (4 - c) / d

Solution

Problem 6 :

The table above shows some values of the linear function f. Which of the following defines f ?

a)  f(n)  = n - 3    b)  f(n) = 2n - 4   c)  f(n) = 3n - 5

d)  f(n) = 4n - 6

Solution

Problem 7 :

The average number of students per classroom at Central High School from 2000 to 2010 can be modeled by the equation y = 0.56x + 27.2, where x represents the number of years since 2000, and y represents the average number of students per classroom. Which of the following best describes the meaning of the number 0.56 in the equation ?

a)  The total number of students at the school in 2000.

b)  The average number of students per classroom in 2000.

c)  The estimated increase in the average number of students per classroom each year.

d)  The estimated difference between the average number of students per classroom in 2010 and in 2000.

Solution

Problem 8 :

For the linear function f, the table shows three values of x and their corresponding values of f(x), which equation defines f(x) ?

a) f(x) = 3x + 29           b)  f(x) = 29x + 32

c)  f(x) = 35x + 29        d)  f(x) = 32x + 35

Solution

Problem 9 :

Hana deposited a fixed amount into her bank account each month. The function f(t) = 100 + 25t gives the amount in dollars, in Hana's bank account after t monthly deposits. What is the best interpretation of 25 in this context ?

a) With each monthly deposit, the amount in Hana's bank account increased by $25.

b)  Before Hana made any monthly deposits, the amount in her bank account was $25.

c)  After 1 monthly deposit, the amount in Hana's bank account was $25

d)  Hana's made a total of 25 monthly deposits.

Solution

Answer Key

1)  3x - y  =  -1

2)  x - 2y  =  6

3)  14x + 4y  =  1

4)  15x + 12y  =  2

5)  k = (d - 4) / c

6)  f(n) = 3x - 5 is the required equation.

7) The average number of students per classroom in 2000. So, option b is correct.

8)  y = 3x + 29

9)  With each monthly deposit, the amount in Hana's bank account increased by $25. So, option a is correct.

Problem 1 :

Find the equation of the straight line whose

(i)  Slope is -4 and passing through (1, 2).

(ii)  Slope is 2/3 and passing through (5, -4).

Problem 2 :

Find the equation of the straight line which passes through the midpoint of the line segment joining

(4, 2) and (3, 1)

whose angle of inclination is 30 degree.

Solution

Problem 3 :

Find the equation of the line in the xy-plane with slope −4 that contains the point (−5,−2).

Problem 4 :

Find the equation of the line that contains the points (2,−1) and (4, 9).

Problem 5 :

Find the equation of the line that contains the points (−3, 2) and (−5, 7).

Solution

Problem 6 :

Find the equation of a straight line whose slope is 7 and which passes through the point (5,-6).

Problem 7 :

Find the equation of a straight line whose slope is 6 and which passes through the point (-1, -2) 

Problem 8 :

Find the equation of a straight line whose slope is 2/3 and which passes through the point (-2,-4) 

Problem 9 :

Find the equation of a straight line whose slope is -1/5 and which passes through the point (-3,-1) 

Problem 10 :

Find the equation of a straight line whose slope is -2/7 and which passes through the point (-5,-4) 

Solution

Problem 11 :

Find the equation of a straight line whose slope is 5 and which passes through the point (1, -3)

Problem 12 :

Find the equation of a straight line whose slope is -1/5 and which passes through the point (4, 8)

Problem 13 :

Find the equation of a straight line whose slope is 1/7 and which passes through the point (-1,8)

Problem 14 :

Find the equation of a straight line whose slope is 2/5 and which passes through the point (0,-7)

Problem 15 :

Find the equation of a straight line whose slope is 5/7 and which passes through the point (-2,-1)

Solution

Answers :

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