Question

Draw the graph of the line that is parallel to Y -3 = 1/3(x+2) and goes through the point (1, 7)

Answer 1

Explanation:

We are required to draw the graph of the line that is parallel to y-3=1/3(x+2) and goes through the point (1, 7).

Given the equation of the line:

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

Compare the equation with the slope-point form of a line:

`$$y-y_1=m(x-x_1)$$`

• The slope of the line, m=1/3

,

• In addition, the line goes through the point (1,7)

Substitute these values into the point-slope form given above:

`y-7=(1)/(3)(x-1)`

Finally, graph the line by looking for another point in addition to point (1,7):

When x=-2

`\begin{gathered} y-7=(1)/(3)(x-1) \\ y-7=(1)/(3)(-2-1) \\ y-7=(1)/(3)(-3) \\ y-7=-1 \\ y=-1+7 \\ y=6 \\ \implies(-2,6) \end{gathered}`

Join the points (1, 7) and (-2, 6) to plot the line.

Answer:

The graph showing the two points is attached below:

Note:

For comparison purposes and to show that the two lines are parallel, the other graph is added below: