Question

find the slope of the line and sketch the graph.
6y = -4x

select the correct choice below and fill in any answer boxes present in your choice.
a. the slope of the line is
(simplify your answer. type an integer or a fraction.)
b. the slope is undefined.

Explanation:

Step1: Recall 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 need to rewrite the given equation \(6y=-4x\) in this form.

Step2: Solve for y

To get \(y\) by itself, we divide both sides of the equation \(6y = - 4x\) by 6. So, \(y=\frac{-4x}{6}\).

Step3: Simplify the fraction

Simplify \(\frac{-4}{6}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 2. \(\frac{-4\div2}{6\div2}=\frac{-2}{3}\). So the equation of the line in slope - intercept form is \(y =-\frac{2}{3}x+0\), and the slope \(m =-\frac{2}{3}\).

Answer:

A. The slope of the line is \(-\frac{2}{3}\)