Question

A line has the equation Y=1/3x-5. Find the equation of a parallel line passing through (3,2).

Answer 1

y=1/3x+1

Step-by-step explanation:

Two lines are parallel if they have the same slope.

Comparing the equation of the line with the slope-intercept form:

`\begin{gathered} y=mx+b \\ y=(1)/(3)x-5 \\ \implies\text{Slope, m}=(1)/(3) \end{gathered}`

Therefore, the line parallel to it has a slope of 1/3.

Thus, using the slope-point form, we find the equation of a line with a slope of 1/3 and passing through (3,2).

`\begin{gathered} y-y_1=m(x-x_1) \\ y-2=(1)/(3)(x-3) \\ y-2=(1)/(3)x-1 \\ y=(1)/(3)x-1+2 \\ y=(1)/(3)x+1 \end{gathered}`

The equation of the parallel line is y=1/3x+1.