Question

Find the equation of a line in slope-intercept from with an x-intercept of 4 and a y-intercept of -3

Answer 1

y=-3x+4

Explanation:

Just plug in y=mx+b

Answer 2

Slope intercept form of line passing through (4, 0) and (0, 8) that means slope intercept form of line having x-intercept of 4 and a y-intercept of -3 is
`y=(3)/(4) x-1`.

Solution:

Need to find the equation of a line in slope intercept form

Given that,

x intercept of line is 4 and y intercept of line = -3 ; x intercept is a point where line crosses the x axis.

In our case line have x intercept of 4, which means line crosses x axis at 4. Another catch here is at x axis, value of y is always 0. So we can say that line passes through point (4, 0).

y intercept is a point where line crosses the y axis. In our case line have y intercept of -3 , which means line crosses y axis at -3.Also at y axis, value of x is always 0.

So we can say that line passes through point (0,-3). Now we can say that we need equation of line passing through (4, 0) and (0, -3)

Equation of line passing through point
`(x_1, y_1) \ and \ (x_2, y_2)` is given by

`y-y_(1)=(\left(y_(2)-y_(1)\right))/(\left(x_(2)-x_(1)\right))\left(x-x_(1)\right) \rightarrow(1)`

In our case
`x_1 = 4; \ y_1=0; \ x_2 = 0; \ y_2 = -3`

Substituting given value in (1) we get ,

`\begin{array}{l}{y-0=((-3-0))/((0-4))(x-4)} \\\\ {\Rightarrow y=(3)/(4)(x-4)} \\\\ {\Rightarrow y=(3)/(4) x-1}\end{array}`

Hence slope intercept form of line passing through (4, 0) and (0, 8) is
`y=(3)/(4) x-1`