Question

(a) draw a scatter plot of the data.
(b) find the equation of the line, in slope-intercept form, containing the points (8,2.3) and (9,2.6).
(c) graph the line found in part (b) on the scatter plot.
x 2 4 5 8 9
y 1.5 1.9 2.1 2.3 2.6

(a) choose the correct scatter plot of the data above.
a.
b.
c.

(b) find the equation of the line, in slope-intercept form, containing the points (8,2.3) and (9,2.6).
y = f(x) =
(use integers or decimals for any numbers in the expression. round to the nearest tenth as needed.)

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). For the points \((8, 2.3)\) and \((9, 2.6)\), we have \( x_1 = 8 \), \( y_1 = 2.3 \), \( x_2 = 9 \), \( y_2 = 2.6 \). So, \( m=\frac{2.6 - 2.3}{9 - 8}=\frac{0.3}{1}=0.3 \).

Step2: Find the y - intercept

Using the slope - intercept form \( y=mx + b \), we can substitute one of the points and the slope to find \( b \). Let's use the point \((8, 2.3)\) and \( m = 0.3 \). Substitute into \( y=mx + b \): \( 2.3=0.3\times8 + b \). Calculate \( 0.3\times8 = 2.4 \). Then, \( 2.3=2.4 + b \). Solve for \( b \): \( b=2.3 - 2.4=- 0.1 \).

Step3: Write the equation

The slope - intercept form of a line is \( y=mx + b \). Substituting \( m = 0.3 \) and \( b=-0.1 \), we get \( y = 0.3x-0.1 \).

Answer:

\( y = 0.3x - 0.1 \)