Given: The equation of the line below
[tex]\begin{gathered} y=\frac{1}{2}x-4 \\ Point:(4,5) \end{gathered}[/tex]To Determine: The equation of the line that is parallel to the given equation of a line
Solution
Please the slope of two parallel lines is the same
Let us determine the slope of the given equation using general slope-intercept form
[tex]\begin{gathered} slope-intercept-form \\ y=mx+c \\ m=slope \\ c=y-intercept \end{gathered}[/tex][tex]\begin{gathered} y=\frac{1}{2}x-4 \\ m=slope=\frac{1}{2} \end{gathered}[/tex]The slope of the parallel line would be same as the line given, which is 1/2
Let us apply the general equation of a line using slope and a point
[tex]\frac{y-y_1}{x-x_1}=slope[/tex]Let us substitute into the formula
[tex]\begin{gathered} Point(x_1,y_1)=(4,5) \\ slope=\frac{1}{2} \\ \frac{y-5}{x-4}=\frac{1}{2} \end{gathered}[/tex][tex]\begin{gathered} y-5=\frac{1}{2}(x-4) \\ y-5=\frac{1}{2}x-\frac{1}{2}\times4 \\ y-5=\frac{1}{2}x-2 \\ y=\frac{1}{2}x-2+5 \\ y=\frac{1}{2}x+3 \end{gathered}[/tex]Hence, the equation of the line