Question

# Write the equations of the given lines.

Line 1: y-intercept = 3, slope = 2

Line 2: y-intercept = - 1, slope = -5

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, where-

y = y-coordinate

m = slope

x = x-coordinate

b = y-intercept

## 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:-

Line 1: y-intercept = b = 3, slope = m = 2

Equation of a line in Slope-intercept form-

y = mx + b

∴ y = 2 × x + 3

∴ y = 2x + 3

Line 2: y-intercept = b = -1, slope = m = -5

Equation of a line in Slope-intercept form-

y = mx + b

∴ y = (-5) × x + (-1)

∴ y = -5x -1

Final Answer:-

∴ y = 2x + 3 and y = -5x - 1 are the equations of the given Line 1 & Line 2, respectively.

### Related Questions to study

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.

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**Note:**

Another answer for this problem could be taken as 137 as well.

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Another answer for this problem could be taken as 137 as well.

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The relation between speed, distance and time given by the relation above is very important. There could be many such questions formed which ask us to calculate any of the three quantities with certain conditions involved.

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**Note:**

The relation between speed, distance and time given by the relation above is very important. There could be many such questions formed which ask us to calculate any of the three quantities with certain conditions involved.