Question

Find the equation of the line that is parallel to Y = 1/2x -4 and contains the point (4,5)

Answer 1

Given: The equation of the line below

`\begin{gathered} y=(1)/(2)x-4 \\ Point:(4,5) \end{gathered}`

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

`\begin{gathered} slope-intercept-form \\ y=mx+c \\ m=slope \\ c=y-intercept \end{gathered}`
`\begin{gathered} y=(1)/(2)x-4 \\ m=slope=(1)/(2) \end{gathered}`

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

`(y-y_1)/(x-x_1)=slope`

Let us substitute into the formula

`\begin{gathered} Point(x_1,y_1)=(4,5) \\ slope=(1)/(2) \\ (y-5)/(x-4)=(1)/(2) \end{gathered}`
`\begin{gathered} y-5=(1)/(2)(x-4) \\ y-5=(1)/(2)x-(1)/(2)*4 \\ y-5=(1)/(2)x-2 \\ y=(1)/(2)x-2+5 \\ y=(1)/(2)x+3 \end{gathered}`

Hence, the equation of the line