Question

Line r is parallel to the graph of 2x-3y=-18 the y intercept of line r is 2 what is the x intercept of line r

Answer 1

x-intercept of line r =
`-3`

Explanation:

The general form of the equation of a straight line is the slope-intercept form:

`y = mx + c`

Where:

m = slope

c = y-intercept

Rearranging the provided equation of graph to make y the subject of the equation:

`2x - 3y = -18`

`2x = -18 + 3y`

`2x + 18 = 3y`

The coefficient of y needs to be
`+1`. Therefore:

`(1)/(3)(2x + 18) = (1)/(3)(3y)`

Expand the parenthesis by using the Distributive Law:

`(2)/(3)x + (18)/(3) = (3)/(3)y`

`(2)/(3)x + 6 = y`

∴Equation of this straight line
`l_(1)`:

`y = (2)/(3)x + 6`

By comparing
`l_(1)` with the general form, it can be deduced that:

the slope m of
`l_(1)` =
`(2)/(3)`

The line r parallel to
`l_(1)` will have the same slope. It is provided that the y-intercept of r is 2. Therefore, the equation of the straight line r is:

`y = (2)/(3)x + 2`

The x-intercept of r can be determined by substituting the value of y = 0:

`0 = (2)/(3)x + 2`

`0 - 2 = (2)/(3)x`

`-2 = (2)/(3) x`

`(-2)/(1) = (2)/(3)x`

Cross-multiplication is applied:

`(-2)(3) = (1)(2x)`

`-6 = 2x`

`(-6)/(2) = (2)/(2)x`

∴x = x-intercept =
`-3`

Answer 2

-3

Explanation:

2x - 3y = -18

Making y subject:

y = 2x/3 + 6

The gradient of line r = 2/3 (parallel to y = 2x/3 + 6)

Since the y intersect is 2

Then y = mx + c ( m = 2/3 and c = 2)

y = 2x/3 + 2

when y = o

x = -3

therefore the x intercept = -3