Grade 10 Math · y = mx + b
The line's uniform
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The line's uniform

Every straight line can wear the same uniform: y=mx+by = mx + b — read aloud, y equals m x plus b. xx is whatever you put in — gigabytes used, weeks grown, kilometres driven — and yy is what comes out, usually the total. Two more numbers tell you everything else. bb is the y-intercept, where the line starts when x=0x = 0: the flat fee, the height on planting day, the fare before the wheels move. And mm is the slope, the charge for every single step of x.

These lines are everywhere money and growth are — phone plans, ride fares, seedlings. The uniform solves for whichever letter the question hides: y=mx+by = mx + b as written, m=ybxm = \dfrac{y - b}{x} for the rate, b=ymxb = y - mx for the start. One line, three questions — and this lesson asks all three.