Question

Give the slope and y-intercept of the given line and then graph it.

8. 2x-3y=6

9. Y=-2x

Answer 1

Give the slope and y-intercept of the given line and then graph it.

8. $2x - 3y = 6$

9. $Y = -2x$

Solution.

8. An equation for the line in point/slope form is

$$y - y _ {0} = k (x - x _ {0}),$$ $$y = k x + y _ {0} - k x _ {0}.$$

In our case we have

$$2 x - 3 y = 6,$$ $$y = \frac {2}{3} x - 2.$$

Then $k = \frac{2}{3}$ . If $x = 0$ then $y = -2$ . And finally we graph this line (figure 1).

9. In this case we have

$$y = - 2 x.$$

Then $k = -2$ . If $x = 0$ then $y = 0$ . And finally we graph this line (figure 2).

Figure 1.

Figure 2