Find the equation of a straight line:(i) with slope 2 and y – interc

1.	Find the equation of a straight line:(i) with slope 2 and y – intercept 3;(ii) with slope – 1/ 3 and y – intercept – 4.(iii) with slope – 2 and intersecting the x–axis at a distance of 3 units to the left of origin.
Answer» (i) With slope 2 and y – intercept 3 The slope is 2 and the coordinates are (0, 3) Now, the required equation of line is y = mx + c Substitute the values, we get y = 2x + 3 (ii) With slope – 1/ 3 and y – intercept – 4 The slope is – 1/3 and the coordinates are (0, – 4) Now, the required equation of line is y = mx + c Substitute the values, we get y = -1/3x – 4 3y + x = – 12 (iii) With slope – 2 and intersecting the x–axis at a distance of 3 units to the left of origin The slope is – 2 and the coordinates are (– 3, 0) Now, the required equation of line is y – y₁ = m (x – x₁) Substitute the values, we get y – 0 = – 2(x + 3) y = – 2x – 6 2x + y + 6 = 0

Find the equation of a straight line:(i) with slope 2 and y – intercept 3;(ii) with slope – 1/ 3 and y – intercept – 4.(iii) with slope – 2 and intersecting the x–axis at a distance of 3 units to the left of origin.

Answer»

(i) With slope 2 and y – intercept 3

The slope is 2 and the coordinates are (0, 3)

Now, the required equation of line is

y = mx + c

Substitute the values, we get

y = 2x + 3

(ii) With slope – 1/ 3 and y – intercept – 4

The slope is – 1/3 and the coordinates are (0, – 4)

Now, the required equation of line is

y = mx + c

Substitute the values, we get

y = -1/3x – 4

3y + x = – 12

(iii) With slope – 2 and intersecting the x–axis at a distance of 3 units to the left of origin

The slope is – 2 and the coordinates are (– 3, 0)

Now, the required equation of line is y – y₁ = m (x – x₁)

Substitute the values, we get

y – 0 = – 2(x + 3)

y = – 2x – 6

2x + y + 6 = 0