Maths-

General

Easy

Question

# Find the slope and write the equation of the given line.

Hint:

### 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

## The correct answer is: Slope of the given line is 1 and equation of the given line is x - y = -2.

### Step-by-step solution:-

From the given diagram, we can observe that the given line passes through 2 points i.e. A(-2,0) and B(0,2)

Hence, x1 = -2, y1 = 0; x2 = 0 & y2 = 2

From the given information, we can observe that the given line passes through points A and B.

Using the 2point formula for slope of a line, we get-

Slope = m = y2 - y1 / x2 - x1

= 2 - 0 / 0 - (-2)

= 2 / 0 + 2

= 2 / 2

Slope = m = 1 ............................................ (Equation i)

We can find the equation of the given line using one of the points that it passes through and its slope.

We take Point (-2,0) i.e. x1 = -2 and y1 = 0 and m = 1 from equation i and write the equation in slope point form as-

y-y1 = m (x-x1)

∴ y - 0 = 1 [x - (-2)]

∴ y - 0 = 1 (x + 2)

∴ y = x + 2

∴ y - x = 2

i.e. x - y = -2 ................................... (Multiplying both sides by -1)

Final Answer:-

∴ Slope of the given line is 1 and equation of the given line is x - y = -2.

Note:-

Alternatively, 2 point form can also be used to find the equation as the given line passes through (-2,0) & (0,2).

X1 = -2, y1 = 0; x2 = 0 & y2 = 2

y - y1 = (y2-y1) (x - x1)

(x2-x1)

y - 0 = (2 - 0) [x - (-2)]

[0 - (-2)]

∴ y = 2 × (x + 2)

0 + 2

∴ y = 2 × (x + 2)

2

∴ y = 1 × (x + 2)

∴ y = x + 2

∴ -2 = x - y

i.e. x - y = -2

Hence, Answer remains the same.

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