Question

What is the y=mx+b form for these points? (2, 3) and (4, 12)

Answer 1

Answer:

$y = \frac{9}{2}x - 7$

Step-by-step explanation:

1 - Use the point-slope formula to get the slope

$Slope = m = \frac{Rise}{Run}= \frac{Change~in~y}{Change~in~x} = \frac{y_2-y_1}{x_2-x_1}$

Explanation: Slope is the change from one point to another and automatically rises, and so if it falls, a negative is tacked on.

y2 is the point farthest to the right, y1 - the farthest to the left, and x's follow the same pattern

Defining each of these variables:

y2 = 12

y1 = 3

x2 = 4

x1 = 2

So plugging into our equation for slope, we get the following

$\frac{y_2-y_1}{x_2-x_1} = \frac{12-3}{4-2} = \frac{9}{2}$

Therefore your slope is $\frac{9}{2} x$ and with that in mind, we can plug-and-chug, as my teachers called it.

2 - Using the slope-intercept formula with the slope and points, find the y-intercept, b by isolating it.

y = (9/2)x + b

Plug an x and y in from either of your points and get b alone to find your intercept

3 = (9/2)2 + b

3 = 18/2 + b <- 9/2 * 2 = 9/2 * 2/1 = (9*2)/I(2*1)

3 = 9 + b

-9  -9

-7 = b

Explanation: If we know our equation, without doubt, passes through a point and we know our slope, then we can know how much variation it is from the base value to reach those points compared to the formula of which that slope passes through the origin, which would be y = mx instead of y=mx+b, by isolating b in this manner.

3 - Plug your slope, m, and your y-intercept, b, back into y = mx + b

y = mx+b

y = (9/2)x + -7

y = (9/2)x - 7

Hope this helps