Question

write the linear equation that gives th
x | y
-40 | -61
-16 | -37
8 | -13
32 | 11
write your answer as an equation with y

Explanation:

Step1: Calculate the slope (m)

We use two points, say \((-40, -61)\) and \((-16, -37)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
So, \(m=\frac{-37 - (-61)}{-16 - (-40)}=\frac{-37 + 61}{-16 + 40}=\frac{24}{24}=1\).

Step2: Use point - slope form to find the equation

We use the point - slope form \(y - y_1=m(x - x_1)\). Let's use the point \((8, - 13)\) and \(m = 1\).
Substitute into the formula: \(y-(-13)=1\times(x - 8)\).
Simplify: \(y + 13=x - 8\).
Then, \(y=x-8 - 13\), so \(y=x - 21\).

We can check with another point, for example, when \(x = 32\), \(y=32-21 = 11\), which matches the table.

Answer:

\(y=x - 21\)