Question

Write the linear equation that gives the rule for this table.

X
4
5
6
7
y
46
60
74
88
Write your answer as an equation with y first, followed by an equals sign.

Answer 1

y = 14x - 2

Explanation:

To write the linear equation that describes the relationship between the variables x and y in this table, we need to find the slope and the y-intercept of the line that represents this relationship.

The slope of a line is a measure of how steep the line is. It is calculated as the change in y divided by the change in x for any two points on the line. In this case, we can see that the y values increase by 14 as the x values increase by 1. Therefore, the slope of the line is 14.

The y-intercept is the point where the line crosses the y-axis. In this case, the y-intercept is the value of y when x is equal to 0. From the table, we can see that when x is 4, y is 46. We can use this information to find the y-intercept by substituting the values into the slope formula:

y - 46 = 14(x - 4)

y - 46 = 14x - 56

y = 14x - 10

We can then rewrite this equation in the form y = mx + b, where m is the slope and b is the y-intercept:

y = 14x - 10

= 14x - 2

Therefore, the linear equation that describes the relationship between x and y in this table is y = 14x - 2.