Question

Choose the equation below that represents the line passing through the point (2, -4) with a slope of one half.

y = one halfx + 5
y = one halfx − 3
y = one halfx − 5
y = one halfx + 3

Answer 1

Answer: y = one half x − 5

Explanation:

We know that , the equation of line that passes through point (a,b) and has slope m is given by :-

`(y-b)=m(x-a)`

Given : Point = (a,b)=(2, -4)

Slope =
`(1)/(2)`

Then, the equation of the line will be (substitute all the values in the above formula) :-

`(y-(-4))=(1)/(2)(x-2)`

`\Rightarrow\ y+4=(1)/(2)(x-2)`

`\Rightarrow\ y+4=(1)/(2)x-1`

Subtract 4 from both sides , we get

`y=(1)/(2)x-1-4`

`y=(1)/(2)x-5`

Hence, the correct answer is y = one half x − 5

Answer 2

y = (1/2)x - 5

Explanation:

Try the answers:

... -4 ≠ (1/2)·2 + 5

... -4 ≠ (1/2)·2 - 3

... -4 = (1/2)·2 - 5 . . . . . the third choice works

... -4 ≠ (1/2)·2 + 3

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You can write the point-slope form equation and simplify.

... y -k = m(x -h) . . . . . . equation for line of slope m through point (h, k)

... y -(-4) = (1/2)(x -2) . . . filled in with your values, m=1/2, (h, k) = (2, -4)

... y = (1/2)x -1 -4 . . . . subtract 4, eliminate parentheses

... y = (1/2)x - 5 . . . . . simplified. (Matches the 3rd selection.)