In three dimensional graphs the z intercept is where the graphed plane intercepts the z axis while both x and y equal 0.
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A z-intercept is a point at which a line crosses the z-axis of a Cartesian grid.
To find the intercepts of the equation 4x - 6y - 5z = 60, we set each variable to zero one at a time. When x = 0 and y = 0, we get -5z = 60, so the z-intercept is z = -12. When x = 0 and z = 0, we get -6y = 60, so the y-intercept is y = -10. When y = 0 and z = 0, we get 4x = 60, so the x-intercept is x = 15.
First, find the LCM (Least Common Multiple) of the three intercepts. Second, divide the LCM by the X-Intercept. Repeat for the Y- and Z-Intercepts. Third, take the three values, and put them together like this: (LCM/X-Intercept)x+(LCM/Y-Intercept)y+(LCM/Z-Intercept)z=LCM If it need it, you can simplify it. For example, if you have a plane with the intercepts (5, 0, 0), (0, 2, 0), and (0, 0, 3), the the LCM would be 30, so you would have: (30/5)x+(30/2)y+(30/3)z=30 6x+15y+10z=30
X-intercept=3 y-intercept=-2
Slope is zero y-intercept is -7 there is no x-intercept for this equation