Question

write the linear equation that gives the rule for this table.
x y
-13 14
11 38
35 62
59 86
write your answer as an equation with y first, followed by an
equals sign.
submit

Explanation:

Step1: Find the slope (m)

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let's take the first two points \( (-13, 14) \) and \( (11, 38) \).
\( m=\frac{38 - 14}{11 - (-13)}=\frac{24}{24} = 1 \)
We can check with another pair, say \( (11, 38) \) and \( (35, 62) \): \( m=\frac{62 - 38}{35 - 11}=\frac{24}{24}=1 \). So the slope \( m = 1 \).

Step2: Find the y-intercept (b)

Using the point-slope form \( y - y_1=m(x - x_1) \), we can use the point \( (-13, 14) \) and \( m = 1 \).
\( y - 14=1\times(x - (-13)) \)
\( y - 14=x + 13 \)
\( y=x + 13+14 \)
\( y=x + 27 \)

Answer:

\( y = x + 27 \)