Mathematics Questions and Answers – General Equation of a Line

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “General Equation of a Line”.

1. Equation of horizontal line above x-axis at 5 units from x-axis is _______
a) x=5
b) x=-5
c) y=5
d) y=-5
View Answer

Answer: c
Explanation: Equation of x-axis is y=0. Horizontal line is parallel to x-axis and above it by 5 units so, equation of line is y=5.
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2. Equation of horizontal line below x-axis at 5 units from x-axis is _______
a) x=5
b) x=-5
c) y=5
d) y=-5
View Answer

Answer: d
Explanation: Equation of x-axis is y=0. Horizontal line is parallel to x-axis and below it by 5 units so, equation of line is y=-5.

3. Equation of vertical line to the right of y-axis at 5 units from y-axis is _______
a) x=5
b) x=-5
c) y=5
d) y=-5
View Answer

Answer: a
Explanation: Equation of y-axis is x=0. Vertical line is parallel to y-axis and to the right by 5 units so, equation of line is x=5.
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4. Equation of vertical line to the left of y-axis at 5 units from y-axis is _______
a) x=5
b) x=-5
c) y=5
d) y=-5
View Answer

Answer: b
Explanation: Equation of y-axis is x=0. Vertical line is parallel to y-axis and to the left by 5 units so, equation of line is x=-5.

5. Find the equation of line parallel to x-axis and passing through (3, 4).
a) x=3
b) x=4
c) y=4
d) y=3
View Answer

Answer: c
Explanation: Let general equation of line be y=m*x + c.
Since line is parallel to x-axis so, m=0.
=>y=c=>y=4 by substituting the point (3, 4).
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6. Find the equation of line parallel to y-axis and passing through (3, 4).
a) x=3
b) x=4
c) y=4
d) y=3
View Answer

Answer: a
Explanation: Let general equation of line be y=m (x-d) => x = y/m +d
Since line is parallel to y-axis so, m=1/0 or 1/m =0
=>x=d => x=3 by substituting the point (3, 4).

7. If a line has slope 3 and pass through point (1, 2) then the equation of line is _________
a) x=3y-1
b) x=3y+1
c) y=3x+1
d) y=3x-1
View Answer

Answer: d
Explanation: Let general equation of line be y=m*x + c.
Given m=3 => y=3x+c
Substituting the point (1, 2) in above equation we get 2=3*1 + c => c = -1
So, equation of line will be y = 3x-1.
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8. Find the equation of line joining (3, 4) and (5, 8).
a) y = 2x-1
b) y = 2x+2
c) y = 2x+1
d) y = 2x-2
View Answer

Answer: d
Explanation: We know, equation of line joining two points (x1, y1) and (x2, y2) is given by
\(\frac{y-y1}{y2-y1} = \frac{x-x1}{x2-x1}\)
So, equation will be \(\frac{y-4}{8-4} = \frac{x-3}{5-3}\)
=>\(\frac{y-4}{4} = \frac{x-3}{2}\)
=>y-4 = 2x-6
=>y = 2x-2

9. If slope of a line is 4 and y-intercept made by the line is 2 then the equation of line will be __________
a) y=4x-2
b) y=4x+2
c) y=2x+4
d) y=2x-4
View Answer

Answer: b
Explanation: Let general equation of line be y=m*x + c.
Given, m=4 and c=2.
=>y=4x+2
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10. If slope of a line is 4 and x-intercept made by the line is 2 then the equation of line will be __________
a) y = 4x-8
b) y = 4x+8
c) y = 2x+4
d) y = 2x-4
View Answer

Answer: a
Explanation: Let general equation of line be y=m*x + c.
Given m=4 and value of x when y=0 is 2.
C= – m*2 = -4*2 = -8.
=>y=4x-8.

11. If x-intercept of a line is 4 and its y-intercept is 2 then find the equation of line.
a) 2x+y-4=0
b) x+2y-4=0
c) 2x+y+4=0
d) x+2y+4=0
View Answer

Answer: b
Explanation: If x-intercept of a line is a and y-intercept of line is b so, equation of line is \(\frac{x}{a} + \frac{y}{b}\) = 1.
Equation of line is \(\frac{x}{4} + \frac{y}{2}\) = 1 => x+2y-4=0.

12. If perpendicular distance of a line from origin is 4 units and angle which the normal makes with positive x-axis is 45°, then the equation will be ______________
a) x + y = 4√2
b) x – y = 4√2
c) y – x = 4√2
d) x + y = -4√2
View Answer

Answer: a
Explanation: If p is perpendicular distance of line from origin and ω be the angle formed by normal with positive x-axis then equation of line is x cos⁡ω + y sin⁡ω = p.
So, equation of given line will be x cos⁡45° + y sin⁡45° = 4
=>(x + y)/√2 = 4
=>x + y = 4√2.

13. If -40°F is equal to -40°C and 0°C is equal to 32°F then find the value of 40°C.
a) 104°F
b) 112°F
c) 86°F
d) 92°F
View Answer

Answer: a
Explanation: Let general equation be F=m*C +k
-40 = -40m + k
and 32 = 0 + k
=>-40 = -40m + 32 => m=72/40 = 18/10
F=18/10 * 40 + 32 = 72+32 = 104.

14. If P (1, 2), Q (3, 5), R (7, 9) form a triangle then find the equation of median through P.
a) 5x-4y+3 = 0
b) 5x+4y+3 = 0
c) 5x-4y-3 = 0
d) 5x+4y-3 = 0
View Answer

Answer: a
Explanation: Midpoint of QR line is \((\frac{3+7}{2}, \frac{5+9}{2})\) = (5, 7).
Equation of line joining (1, 2) and (5, 7) is \(\frac{y-2}{7-2} = \frac{x-1}{5-1}\)
=>\(\frac{y-2}{5} = \frac{x-1}{4}\) => 4y-8 = 5x-5 => 5x-4y+3 =0.

15. Line perpendicular to line joining (1, 3) and (4, 5) and pass through (2, 4) has equation ____________
a) 3x+2y-14=0
b) 3x-2y-14=0
c) 2x-3y-14=0
d) 2x+3y-14=0
View Answer

Answer: a
Explanation: Slope of line joining (1, 3) and (4, 5) is (5-3) / (4-1) = 2/3
So, slope of line perpendicular to it is -3/2.
Line has slope -3/2 and pass through (2, 4)
So, equation is y-4 = (-3/2)(x-2) => 2y-8 = -3x+6 => 3x+2y-14=0.

Sanfoundry Global Education & Learning Series – Mathematics – Class 11.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter