Tell whether the graphs of the two equations are parallel lines, x-3y=6, y=-1/3x

Question

Tell whether the graphs of the two equations are parallel lines.

Answer 1

Write the equations in slope-intercept form y = mx + b, where m is slope and b is y - intercept.

The first equation is x - 3y = 6.

- 3y = - x + 6

y = (1/3)x - 2.

Compare the equation with slope-intercept form y = mx + b.

slope = 1/3 and y-intercept is - 2.

y-intercept is - 2, so the line crosses the y-axis at (0, - 2)

Using slope find the next point.

Slope = rise/run = 1/3

Start at point (0, - 2), move 1 unit up and 3 units right, then plot the point (3, - 1).

The second equation is y = - 1/3 x

Compare the equation with slope-intercept form y = mx + b.

slope = - 1/3 and y-intercept is 0.

y-intercept is 0, so the line crosses the y-axis at origin (0, 0).

Using slope find the next point.

Slope = rise/run = - 1/3 = 1/- 3

Start at point (0, 0), move 1 unit down and 3 units right, then plot the point (-3, 1).

Draw the lines through these points.

Graph :

Observe the graph, given lines are not a parallel lines.

They are intersect at a point, i.e, (x, y ) = (3, - 1).