Question

for the straight line defined by the points (1, 55) and (3, 87), determine the slope (m) and y-intercept (b). do not round the answers.

m =

b =

Explanation:

Step1: Calculate the slope (m)

The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Here, \((x_1, y_1) = (1, 55)\) and \((x_2, y_2) = (3, 87)\).
\[m = \frac{87 - 55}{3 - 1} = \frac{32}{2} = 16\]

Step2: Find the y-intercept (b)

Use the slope-intercept form \(y = mx + b\). Substitute \(m = 16\), \(x = 1\), and \(y = 55\) into the equation.
\[55 = 16(1) + b\]
\[55 = 16 + b\]
Subtract 16 from both sides:
\[b = 55 - 16 = 39\]

Answer:

\(m = 16\)
\(b = 39\)