Question

Write an equation of a line in standard form for the given conditionsx-intercept= -1 and y-intercept=4a.4x-y=-4b.4x-y=-11c.y=-4x-7d.4x+y=-11e.4x+y=-4f.y=4x-7

Answer 1

A line is said to have an x-intercept of -1, and a y-intercept of 4.

It is required to write the equation of the line in standard form.

Recall that the Standard Form of the equation of a line is of the form:

`Ax+By=C`

The equation of a line with slope m and y-intercept c in slope-intercept form is:

`y=mx+c`

Since the y-intercept is 4, substitute c=4 into the equation:

`\Rightarrow y=mx+4`

Since the x-intercept is -1, substitute x=-1 and y=0 into the equation to find m:

`\begin{gathered} \Rightarrow0=m(-1)+4 \\ \Rightarrow0=-m+4 \\ \Rightarrow m=4 \end{gathered}`

Substitute m=4 back into the equation:

`\begin{gathered} \Rightarrow y=4x+4 \\ \text{ Rewrite in the standard form:} \\ \Rightarrow-4x+y=4 \\ \text{ Multiply both sides by }-1: \\ \Rightarrow4x-y=-4 \end{gathered}`

The correct option is a.