Question
The slope of a line is –½ and it passes through origin. Find its equation.
Hint:
1. The slope of a line can be defined as the change in y coordinates of any 2 points on that line corresponding to the change in the x coordinates of those 2 points. This is generally referred to as the rise to run ratio of the given line i.e. how much did the y-coordinates rise vis-a-vis how long a distance was covered by the x-coordinates.
2. A point is said to be on a given line when the coordinates of that point when substituted in the given equation, satisfies the given equation.
3. Equation of a line in slope point form can be written as-
(y-y1) = m (x-x1)
The correct answer is: 2y + x = 0 is the equation of the line with slope -1/2 and passing through origin.
Step-by-step solution:-
The given line has a slope of -1/2 and it passes through the origin O (0,0).
∴ x1 = 0, x2 = 0 & m = -1/2
Now, we know that equation of a line in slope point form-
(y-y1) = m (x-x1)
∴ (y-0) = -1/2 (x-0)
∴ y = -1/2 × x
∴ y = -1/2 x
∴ 2y = -1x ................. (Multiplying both sides by 2)
∴ 2y + x = 0
Final Answer:-
∴ 2y + x = 0 is the equation of the line with slope -1/2 and passing through origin.
Related Questions to study
A water pipe is a cylinder 30 inches long, with a radius of 1 inch. At one end of the cylinder there is a hemisphere. What is the volume of the water pipe?
A water pipe is a cylinder 30 inches long, with a radius of 1 inch. At one end of the cylinder there is a hemisphere. What is the volume of the water pipe?
The graph shows the subscription cost to a certain club in town. Write an equation of the
line. Explain what the slope and y-intercept mean in this situation. Then find the total
cost for 2 years.
The graph shows the subscription cost to a certain club in town. Write an equation of the
line. Explain what the slope and y-intercept mean in this situation. Then find the total
cost for 2 years.
Find a value for k so that the line through (k, 6) and (4, 2) is perpendicular to the line with equation x + 2y = 2.
Find a value for k so that the line through (k, 6) and (4, 2) is perpendicular to the line with equation x + 2y = 2.
Find a value for k so that the line through (35, k) and (42, 27) is parallel to the line with equation y = x.
Find a value for k so that the line through (35, k) and (42, 27) is parallel to the line with equation y = x.
Find the equation of line such that its y-intercept is 20 and slope is ½.
Find the equation of line such that its y-intercept is 20 and slope is ½.
A line passes through the points (-6, 4) and (-2,8). Where does the line intersect the X-axis and the Y-axis?
A line passes through the points (-6, 4) and (-2,8). Where does the line intersect the X-axis and the Y-axis?
The difference between the sides at right angles in right angled triangle is 14 cm. The area of triangle is 120 cm2 . Calculate the perimeter of triangle
The difference between the sides at right angles in right angled triangle is 14 cm. The area of triangle is 120 cm2 . Calculate the perimeter of triangle
The ratio of the diameter and height of a cylinder is 4 : 5. Find the height of the cylinder, if its volume is 540π cubic units.
The ratio of the diameter and height of a cylinder is 4 : 5. Find the height of the cylinder, if its volume is 540π cubic units.
Identify the parallel lines and perpendicular lines from the given set.
2x + y = 1
9x + 3y = 6
y = 3x
y = -3x
2y = 4x +6
Y = - x/2
Identify the parallel lines and perpendicular lines from the given set.
2x + y = 1
9x + 3y = 6
y = 3x
y = -3x
2y = 4x +6
Y = - x/2
Carrie, a packaging engineer, is designing a container to hold 12 drinking glasses shaped as regular octagonal prisms. Her initial sketch of the top view of the base of the container is shown above.
Carrie redesigned the container because the initial sketch did not account for cushioning material between the glasses. The area of the base of the newly designed container is 
greater than the area of the base in the initial sketch. What is the area, in square inches, of the base of the newly designed container?
Note:
There is a shorter way of doing this problem. There is a simple rule followed while increasing or decreasing a value by a certain percentage. When we decrease a quantity by x%, we multiply the quantity by (1-0.x). Whereas when we increase a quantity by x%, we multiply it with (1+0.x).
Carrie, a packaging engineer, is designing a container to hold 12 drinking glasses shaped as regular octagonal prisms. Her initial sketch of the top view of the base of the container is shown above.
Carrie redesigned the container because the initial sketch did not account for cushioning material between the glasses. The area of the base of the newly designed container is greater than the area of the base in the initial sketch. What is the area, in square inches, of the base of the newly designed container?
Note:
There is a shorter way of doing this problem. There is a simple rule followed while increasing or decreasing a value by a certain percentage. When we decrease a quantity by x%, we multiply the quantity by (1-0.x). Whereas when we increase a quantity by x%, we multiply it with (1+0.x).
Find the equation of line that passes through the point (2, -9) and which is perpendicular to the line x = 5.
Use the perpendicular line formula to determine whether two given lines are perpendicular. For example, when the slope of two lines is given to compare, we can use the perpendicular line's formula. A 90-degree angle is created by two lines that are perpendicular to one another.
Slope exists on every line. Because it shows how quickly our line is rising or falling, the slope of a line reveals how steep a line is. Mathematically, the slope of a line is known as the ratio of change in the line's y-value to the change in its x-value.
¶A line's slope can be determined using its two points (x1, y1) and (x2, y2). The formula (y2 - y1) / is used to find the change in y and divided by the change in x. (x2 - x1).
Find the equation of line that passes through the point (2, -9) and which is perpendicular to the line x = 5.
Use the perpendicular line formula to determine whether two given lines are perpendicular. For example, when the slope of two lines is given to compare, we can use the perpendicular line's formula. A 90-degree angle is created by two lines that are perpendicular to one another.
Slope exists on every line. Because it shows how quickly our line is rising or falling, the slope of a line reveals how steep a line is. Mathematically, the slope of a line is known as the ratio of change in the line's y-value to the change in its x-value.
¶A line's slope can be determined using its two points (x1, y1) and (x2, y2). The formula (y2 - y1) / is used to find the change in y and divided by the change in x. (x2 - x1).
Write the equations of the given lines.
Line 1: y-intercept = 3, slope = 2
Line 2: y-intercept = - 1, slope = -5
Write the equations of the given lines.
Line 1: y-intercept = 3, slope = 2
Line 2: y-intercept = - 1, slope = -5
Carrie, a packaging engineer, is designing a container to hold 12 drinking glasses shaped as regular octagonal prisms. Her initial sketch of the top view of the base of the container is shown above.
If the length and width of the container base in the initial sketch were doubled, at most how many more glasses could the new container hold?
Note:
A few simple ideas are used in solving this problem, like, area of a rectangle is given by the product of its length and breadth and the basic idea of division.
Carrie, a packaging engineer, is designing a container to hold 12 drinking glasses shaped as regular octagonal prisms. Her initial sketch of the top view of the base of the container is shown above.
If the length and width of the container base in the initial sketch were doubled, at most how many more glasses could the new container hold?
Note:
A few simple ideas are used in solving this problem, like, area of a rectangle is given by the product of its length and breadth and the basic idea of division.
