Question

How do you write the equation of line given x-intercept of 4 and a slope of 3/4?

Answer 1

`y=3/4x-3`

Explanation:

The equation of a line in `color(blue)"slope-intercept form"` is

`color(red)(|bar(ul(color(white)(a/a)color(black)(y=mx+b)color(white)(a/a)|)))`
where m represents the slope and b, the y-intercept.

Here we have a coordinate point (4 ,0) and `m=3/4`

So the partial equation is `y=3/4x+b` and to find b we substitute x = 4 and y = 0 into the partial equation.

`rArr0=3/cancel(4)xxcancel(4)+b=3+brArrb=-3`

`rArry=3/4x-3" is the equation"`

Answer 2

`y=3/4x-3`

Explanation:

Let `color(purple)(k)` be some constant such that
`color(white)("XXX")y=color(green)(m)x+color(purple)(k)`
where `color(green)(m)` is the slope.

We are told that `color(green)(m)=color(green)(3/4)`
and
the x-intercept is `color(brown)(4)`

If the x-intercept is `color(brown)(4)`
this means that `x=color(brown)(4)` when `y=color(cyan)0`

So our general equation: `y=color(green)(m)x+color(purple)(k)`
becomes
`color(white)("XXX")color(cyan)(0)=color(green)(3/4)*color(brown)(4)+color(purple)(k)`

`color(white)("XXX")rarr color(purple)(k)=color(blue)(-3)`

and our equation is
`color(white)("XXX")y=color(green)(3/4)xcolor(blue)(-3)`

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Using the above logic we can see that the general case when given
a slope of `color(green)(m)` and
an x-intercept of `color(purple)(k)`
is
`color(white)("XXX")y=color(green)(m)xcolor(blue)(-k/m)`