Maths-

General

Easy

Question

# If the equation of a line is 2x – 3y = 6, find its slope and y-intercept.

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

## The correct answer is: Slope and y-intercept of the given line are 2/3 and -2, respectively.

### Step-by-step solution:-

2x - 3y = 6

∴ 2x - 6 = 3y

∴ (2x - 6) / 3 = y ….................... (Dividing both sides by 3)

∴ 2/3 x - 6/3 = y

∴ 2/3 x - 2 = y

i.e. Y = 2/3 x - 2 …........................... (Equation i)

Comparing Equation i with the slope intercept form of a line i.e. y = mx + b, we get-

m = 2/3 and b = -2

Final Answer:-

∴ Slope and y-intercept of the given line are 2/3 and -2, respectively.

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