Question

Write the equation of the line with x-intercept 3 and passing through the point (5, 4) ? A) y − 2 = 1 2 (x − 4) B) y + 2 = 2(x + 4) C) y − 2 = 2(x − 4) D) y − 2 = 1 2 (x − 4)

I Don't understand the question, please help.

Answer 1

The line is `y=2x-6`.

Explanation:

We can find out the equation of the line by using the slope formula because we already know two points on the line: `(3,0)` (the `x`-intercept) and `(5,4)`.

`color(white)=>m=(y_2-y_1)/(x_2-x_1)`

`=>m=(4-0)/(5-3)`

`color(white)=>m=4/2`

`color(white)=>m=2`

Now, using point-slope form, we can use the slope and the points that we know to create an equation for the line.

`color(white)=>y-y_1=m(x-x_1)`

`=>y-4=2(x-5)`

You could leave it like this, or you could convert it to slope-intercept form by expanding a little further:

`y-4=2(x-5)`

`y-4=2x-10`

`y=2x-6`

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Answer 2

Neither of them

Explanation:

`y=2x-6` is the equation you're looking for; however, it is not found in any of the answers, assuming the x-intercept is `x=3`.
We can rewrite the equation, though, to best fit the answers (to compare).
Get rid of the -6 on the right side:
`y+6=2x-6+6`
`y+6=2x`
As you can see, the correct answer is not shown.