Question

(a) draw a scatter plot of the data.
(b) find the equation of the line, in slope-intercept form, containing the points (4,1.7) and (5,2.1).
(c) graph the line found in part (b) on the scatter plot.

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

Explanation:

Step1: Calculate the slope

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Given the points \((x_1,y_1)=(4,1.7)\) and \((x_2,y_2)=(5,2.1)\), then \(m=\frac{2.1 - 1.7}{5 - 4}=\frac{0.4}{1}=0.4\)

Step2: Find the y - intercept

Use the point - slope form \(y - y_1=m(x - x_1)\). Substitute \(m = 0.4\), \(x_1 = 4\), \(y_1=1.7\) into \(y - y_1=m(x - x_1)\), we get \(y-1.7 = 0.4(x - 4)\). Expand it: \(y-1.7=0.4x-1.6\). Then \(y=0.4x+0.1\)

Answer:

The equation of the line in slope - intercept form is \(y = 0.4x+0.1\)