Question

Type an equation for the following pattern....

x=1,2,3,4,5
y=28,56,84,112,140

y=?x + ?

Answer 1

y = 28x

Explanation:

In the slope-intercept form of a line, the standard equation is y = mx + b, where m is the slope and b is the y-intercept. This y-intercept value can be found where x = 0.

From our data, we can see that x is going up by 1 unit, and y is going up by 28 units. That is our rate of change, or slope...28. However, we can apply the slope formula to 2 points in that data and check ourselves:

`m=(56-28)/(2-1)=28`

Let's check another 2 points just to be sure the slope is constant:

`m=(84-56)/(3-2)=28`

Ok, so the slope is definitely 28; m = 28

Again we go back to the idea that the b value is the y-intercept, and by definition, the y-intercept exists where x = 0. If we look at where our data starts and then subtract 1 from x and 28 from y, we have x = 0 and also y = 0. The coordinate for that is (0, 0). Here, x = 0, so the y value is our y-intercept (aka b value). b = 0. Therefore, the equation for this data is a line:

y = 28x + 0 or simply, y = 28x