What is the slope and the y-intercept of the line on the graph below?
1 answer:
Well, since we do not know the line, the basic slope formula is Y = mX + B
So look at the line and see where is crosses the y axis (the vertical) and that is your B in the formula or the "Y-intercept" as an example I will used the number 1. Then on your line pick two points, I will use the points (4,4) and (1,2) as an example. To find your slope take the Ys in those points (the second number) and subtract them 4 - 2 = 2. Then subtract the Xs (the first numbers) 4 - 1 = 3. Lastly, take the 2 and divide it by the 3 (yes it can be a fraction) and that is your slope. So the entire answer with my examples would be Y =
x + 1 with 1 being my y-intercept and 2/3 being my slope
So look at the line and see where is crosses the y axis (the vertical) and that is your B in the formula or the "Y-intercept" as an example I will used the number 1. Then on your line pick two points, I will use the points (4,4) and (1,2) as an example. To find your slope take the Ys in those points (the second number) and subtract them 4 - 2 = 2. Then subtract the Xs (the first numbers) 4 - 1 = 3. Lastly, take the 2 and divide it by the 3 (yes it can be a fraction) and that is your slope. So the entire answer with my examples would be Y =
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f(0) = 2(3)(0) = 0 ⇒ (0, 0)
f(1) = 2(3)(1) = 6 ⇒ (1, 6)
<u>rate of change from x = 0 to x = 1</u>
=
=
= 6
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f(2) = 2(3)(2) = 12 ⇒ (2, 12)
f(3) = 2(3)(3) = 18 ⇒ (3, 18)
<u>rate of change from x = 2 to x = 3</u>
=
=
= 6
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Since it is the same line, they will have the same slope (aka rate of change).