Question

The line is parallel to the line y = 1/2x-3, and contains the point (6,5)

Answer 1

Given: Equation of a line

`y=(1)/(2)x-3`

Required: To find the equation of the line that is parallel to the given line and contains the point (6,5).

Explanation: The slopes of the parallel lines are equal. Moreover, the general equation of a line is

`y=mx+c`

Comparing the equation of the given line with the general equation of the line, we get,

`Slope,m=(1)/(2)`

Hence, the required line has a slope of 1/2. It is given that this line contains the point (6,5).

Using the slope point equation of a line-

`y-y_0=m(x-x_0)`

Putting the values, we get,

`\begin{gathered} y-5=(1)/(2)(x-6) \\ 2y-10=x-6 \\ 2y=x+4 \\ y=(1)/(2)x+2 \end{gathered}`

Final Equation: The equation of the line is

`y=(1)/(2)x+2`

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