Question

for the data given below, answer parts (a) through (d)

x	-19	-16	-14	-13	-9
y	102	122	120	132	142

(a) find the equation of the line containing the first and the last data points.
y = \square
(type your answer in slope - intercept form. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Identify the points

The first data point is \((x_1, y_1)=(-19, 102)\) and the last data point is \((x_2, y_2)=(-9, 142)\).

Step2: Calculate the slope \(m\)

The formula for slope is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Substituting the values:
\(m=\frac{142 - 102}{-9 - (-19)}=\frac{40}{10} = 4\)

Step3: Use point - slope form to find the equation

The point - slope form is \(y - y_1=m(x - x_1)\). Using the point \((-19,102)\) and \(m = 4\):
\(y-102=4(x + 19)\)
Expand the right - hand side: \(y-102=4x+76\)
Add 102 to both sides: \(y=4x+76 + 102\)
Simplify: \(y = 4x+178\)

Answer:

\(y = 4x + 178\)