is x-7y=2 a function

how do you know it represents a line

To determine if the equation x - 7y = 2 represents a function, we need to check if each input value (x) corresponds to a unique output value (y).

To do this, let's solve the equation for y in terms of x:

x - 7y = 2

Subtract x from both sides:

-7y = 2 - x

Divide both sides by -7:

y = (2 - x)/(-7)

Since every value of x will result in a unique value of y, the equation x - 7y = 2 represents a function.

To determine whether the equation x-7y=2 represents a function, we need to examine its characteristics.

In order for an equation to be a function, there should be only one unique y-value for each x-value. In other words, no x-value should be associated with multiple y-values.

To check this, we can use the vertical line test. If a vertical line passes through the graph of the equation at most once, then the equation represents a function.

To rewrite the equation in terms of y:
x - 7y = 2
-7y = -x + 2
y = (1/7)x - (2/7)

Now, let's consider the equation in terms of the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. In this form, the coefficient of x represents the slope, which determines the rate at which y changes with respect to x.

In our equation, the coefficient of x is 1/7, so the slope is 1/7. Since the slope is non-zero, the equation does not represent a vertical line, which means it passes the vertical line test. Therefore, x-7y=2 represents a function.

yes,

your equation represents a straight line which is not vertical, so it is a function.