Question

what is the slope of the line with equation $6y - 16x = 7$?
a. $\frac{8}{3}$
b. $16$
c. $-16$
d. $6$
e. $\frac{7}{6}$

Explanation:

Step1: Rewrite in slope - intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We start with the equation \(6y-16x = 7\). First, we need to solve for \(y\).
Add \(16x\) to both sides of the equation: \(6y=16x + 7\).

Step2: Solve for y

Divide each term in \(6y = 16x+7\) by \(6\). So \(y=\frac{16}{6}x+\frac{7}{6}\). Simplify \(\frac{16}{6}\) to \(\frac{8}{3}\). So the equation of the line is \(y = \frac{8}{3}x+\frac{7}{6}\). In the slope - intercept form \(y = mx + b\), the coefficient of \(x\) (i.e., \(m\)) is the slope. So the slope \(m=\frac{8}{3}\).

Answer:

a. \(\frac{8}{3}\)