Graph the line with slope 1/3 passing through the point (2, - 5).

Answer 1

To graph the line with slope 1/3 passing through the point (2, -5), we can use the point-slope form of a line:

y - y1 = m(x - x1)

where m is the slope, and (x1, y1) is a point on the line. Substituting m = 1/3, x1 = 2, and y1 = -5, we get:

y - (-5) = (1/3)(x - 2)

Simplifying and rearranging, we get the slope-intercept form of the line:

y = (1/3)x - (11/3)

Now we can plot the point (2, -5) and use the slope to find another point on the line. The slope of 1/3 means that for every increase of 1 in the x-coordinate, the y-coordinate increases by 1/3. So we can add 3 to the x-coordinate of the point (2, -5) to get a new point with y-coordinate -4:

(2, -5) --> (5, -4)

Plotting these two points and connecting them with a straight line gives us the graph of the line with slope 1/3 passing through the point (2, -5):