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:
[tex]Ax+By=C[/tex]The equation of a line with slope m and y-intercept c in slope-intercept form is:
[tex]y=mx+c[/tex]Since the y-intercept is 4, substitute c=4 into the equation:
[tex]\Rightarrow y=mx+4[/tex]Since the x-intercept is -1, substitute x=-1 and y=0 into the equation to find m:
[tex]\begin{gathered} \Rightarrow0=m(-1)+4 \\ \Rightarrow0=-m+4 \\ \Rightarrow m=4 \end{gathered}[/tex]Substitute m=4 back into the equation:
[tex]\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}[/tex]The correct option is a.
