Question

What is the equation of the line whose y-intercept is 3 and slope is 1? y = x - 3 y = x 3 y = 3x 1 user: what is the slope of a line perpendicular to the line whose equation is y = 2x 5? slope = -1 slope = -1/2 slope = -2

Answer 1

a)

y = mx + c

y = 1x + 3

y = x + 3

b)
y = 2x ? 5 comparing to y = mx + c, slope = m

slope = 2.

But for a perpendicular line, we take the negative reciprocal,

= -1/2 = -1/2

Answer 2

1) The equation of the line whose y-intercept is 3 and slope is 1 is given by
`y=x+3`

2) The slope of a line perpendicular to the line whose equation is
`y=2x+5` is
`-(1)/(2)`

Explanation:

1) To find : What is the equation of the line whose y-intercept is 3 and slope is 1?

Solution :

The general slope form of the line is
`y=mx+c`

Where, m is the slope m=1

and c is the y-intercept c=3

Substitute in the equation of line,

`y=(1)x+3`

`y=x+3`

Therefore, The equation of the line whose y-intercept is 3 and slope is 1 is given by
`y=x+3`

2) To find : What is the slope of a line perpendicular to the line whose equation is
`y = 2x+5`?

Solution :

When two lines are perpendicular the slope of one equation is negative reciprocal of another slope of equation.

The slope of given equation is 2.

The negative reciprocal is
`-(1)/(2)`

Therefore, The slope of a line perpendicular to the line whose equation is
`y=2x+5` is
`-(1)/(2)`