Question

Write an equation of a line in slope-intercept form that passes through (-3,5) and is parallel to y = -6x +1.

Then find its x- and y-intercepts.

Answer 1

a) The equation of the Parallel line to the given straight line is

6 x + y + 13 =0

b) Slope - intercept form

y = - 6 x - 13

c) The intercept - form

`(x)/((-13)/(6) ) + (y)/(-13) = 1`

x - intercept =
`(-13)/(6)`

y - intercept = - 13

Explanation:

Step(i):-

Given the equation of the straight line

y = -6x +1

6 x + y - 1 = 0

The equation of the Parallel line to the given straight line is

6x + y + k=0 and it passes through the point (-3, 5 )

⇒ 6 (-3 ) + 5 + k =0

⇒ - 18 + 5 + k=0

⇒ -13 + k = 0

⇒ k = 13

The equation of the Parallel line to the given straight line is

6 x + y + 13 =0

Step(ii):-

Slope - intercept form

y = m x + C

y = - 6 x - 13

Step(iii):-

Intercept - form

6 x + y + 13 =0

6 x + y = - 13

`(6x + y)/(-13) = (-13)/(-13)`

`(6x)/(-13) + (y)/(-13) = 1`

`(x)/((-13)/(6) ) + (y)/(-13) = 1`

The intercept - form

`(x)/((-13)/(6) ) + (y)/(-13) = 1`

x - intercept =
`(-13)/(6)`

y - intercept = - 13