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

$y=\frac{1}{2}x-3$

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,

$Slope,m=\frac{1}{2}$

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,

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

Final Equation: The equation of the line is

$y=\frac{1}{2}x+2$

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