The x intercept is where the graph crosses the x axis and this happens whenever y = 0.
To find the x intercept, plug in y = 0 and solve for x
y = (-1/5)x+6
(-1/5)x+6 = y
(-1/5)x+6 = 0
(-1/5)x = -6
-x = 5*(-6)
-x = -30
x = 30
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If you plugged x = 30 into y = (-1/5)x+6, then you'd get y = 0
y = (-1/5)x+6
y = (-1/5)(30)+6
y = -6+6
y = 0
