Darren is finding the equation in the form [tex]y = mx + b[/tex] for a trend line that passes through the points [tex](2, 18)[/tex] and [tex](-3, 8)[/tex]. Which value should he use as [tex]b[/tex] in his equation?
A. \(-34\) B. \(-19\) C. \(2\) D. [tex]\(14\)[/tex]
To find the equation of a line in the slope-intercept form \( y = mx + b \) that passes through the points \((2, 18)\) and \((-3, 8)\), we need to follow these steps:
1. Calculate the slope \(m\): The slope \(m\) of the line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula: [tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex] Substituting the given points \((2, 18)\) and \((-3, 8)\): [tex]\[
m = \frac{8 - 18}{-3 - 2} = \frac{-10}{-5} = 2
\][/tex]
2. Use one of the points to find the y-intercept \(b\): We can use the point \((x_1, y_1)\) and the slope to find the y-intercept \(b\) using the equation: [tex]\[
y = mx + b
\][/tex] Rearrange this to solve for \(b\): [tex]\[
b = y - mx
\][/tex] Use the point \((2, 18)\) and the slope \(m = 2\): [tex]\[
b = 18 - 2 \cdot 2 = 18 - 4 = 14
\][/tex]
Therefore, the value Darren should use as [tex]\(b\)[/tex] in his equation is [tex]\( \boxed{14} \)[/tex].
