What are the x- and y-intercepts of the linear function 6x - 3y equals 18?

Answer 1

Once you find the y-intercept(s) you'll be steps away from finding the x-intercept(s). The original equation is 6x - 3y = 18.

Step 1 is to solve for y by isolating y on one side of the equation.

6x - 3y = 18

-3y = 18 - 6x

-3y = -6x + 18

The reason I reorganized the terms, is so that the equation is in the Slope-Intercept form.

y = (-6x/-3) + (18/-3)

y = 2x + (-6)

y = 2x - 6

This equation is in the Slope-Intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. So the y-intercept is -6. Now onto the x-intercept. To get x-intercept(s), keep the equation in the Slope-Intercept form and set y equal to zero.

y = 2x - 6

0 = 2x - 6

0 + 6 = 2x

6 = 2x

6/2 = x

3 = x

So the x-intercept is 3. Now what does these two intercepts tell you? On a graph with a y- and x-axis, when x = 0 then y = -6, which means one of the points on your line is at (0 , -6). The same thing is true for the x-intercept. When y = 0 then x = 3, and that is where your second point is, at (3 , 0). Connect those two points and you'll have your line.