Question

# Find the equation of line such that its y-intercept is 20 and slope is ½.

## The correct answer is: y = 1/2 x + 20 is the equation of the given line

### 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. Slope = m = rise / run = y2-y1 / x2-x1

2. Y-intercept is that point on a line where the line intersects with the y-axis i.e. the point at which x-coordinate is 0.

3. Equation of a line, when its slope and intercept is given can be given as-

y = mx + b

Step-by-step solution:-

We are given that-

Slope of the given line = m = 1/2

and y-intercept = b = 20

Using Slope intercept form of a line, we can find the equation of the given line as-

y = mx + b

∴ y = 1/2 x + 20

Final Answer:-

∴ y = 1/2 x + 20 is the equation of the given line.

### Related Questions to study

### 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 cm^{2} . 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 cm^{2} . 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 (x_{1}, y_{1}) and (x_{2}, y_{2}). The formula (y_{2} - y_{1}) / is used to find the change in y and divided by the change in x. (x_{2} - x_{1}).

### 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 (x_{1}, y_{1}) and (x_{2}, y_{2}). The formula (y_{2} - y_{1}) / is used to find the change in y and divided by the change in x. (x_{2} - x_{1}).

### 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.