Question

(a) draw a scatter plot of the data.
(b) find the equation of the line, in slope - intercept form, containing the points (2,1.3) and (5,1.9).
(c) graph the line found in part (b) on the scatter plot.

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

Explanation:

Step1: Calculate the slope \(m\)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Given \((x_1,y_1)=(2,1.3)\) and \((x_2,y_2)=(5,1.9)\), then \(m=\frac{1.9 - 1.3}{5 - 2}=\frac{0.6}{3}=0.2\).

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

Use the point - slope form \(y - y_1=m(x - x_1)\). Substitute \(m = 0.2\), \(x_1=2\), \(y_1 = 1.3\): \(y-1.3=0.2(x - 2)\). Expand: \(y-1.3=0.2x-0.4\). Add \(1.3\) to both sides: \(y=0.2x+(1.3 - 0.4)\), so \(y = 0.2x+0.9\).

Answer:

The equation of the line in slope - intercept form is \(y = 0.2x + 0.9\).