Question

use the table to answer the question.
this table
shows the
relationship
between x
and y
values that
will
contribute
to linear
functions.

x	y
15	43

write the equation of the linear function that models the relationship shown in the table. enter your answer in $y = mx + b$ form.
(1 point)
$y = \square x - \square$

Explanation:

Step1: Find the slope \( m \)

The formula for slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using the points \( (6, 16) \) and \( (15, 43) \), we have \( x_1 = 6,y_1 = 16,x_2 = 15,y_2 = 43 \). So \( m=\frac{43 - 16}{15 - 6}=\frac{27}{9}=3 \).

Step2: Find the y - intercept \( b \)

Use the point - slope form \( y - y_1=m(x - x_1) \) with \( m = 3 \), \( x_1 = 6 \), \( y_1 = 16 \). Substitute these values into the formula: \( y-16 = 3(x - 6) \). Expand the right - hand side: \( y-16=3x-18 \). Then add 16 to both sides to solve for \( y \): \( y=3x - 2 \).

Answer:

\( y = 3x-2 \)