Determine a relationship between the x- and y-values. Write the resulting equation.

{(2, -12), (3, -18), (4, -24), (5, -30)}

Type your answer as an equation for the value of y, like this: y = -4x + 1

Question

Determine a relationship between the x- and y-values. Write the resulting equation.

{(2, -12), (3, -18), (4, -24), (5, -30)}

Type your answer as an equation for the value of y, like this: y = -4x + 1

displayerror · Answer

We can use the equation for the slope of a line here:
$$Slope = \frac{Rise}{Run} = \frac{y_2 - y_1}{x_2 - x_1}$$
Looking at each set of points, we see the that the x-coordinate (the first number) increases by 1 (2, 3, 4, 5) and the y-coordinate (the second number) decreases by 6 (-12, -18, -24, -30). That suggests that all four points lie on the same line. 
Plugging in each set of points to the slope equation, you should find that the slope is equal to -6:
$$\frac{-12 - (-18)}{2-3} = \frac{-18 - (-24)}{3-4} = \ldots = -6$$
Recall the point-slope form of the equation of a line:
$$y - y_1 = m(x - x_1)$$
This form is useful because we know the slope and we are given a point (hence the name, point-slope form). Plug in any point and the slope that you found and solve for y to get your equation in slope-intercept form (what was mentioned in the directions for your question).