Question

Find the slope and the y-intercept of the line. $$6 x+2 y=14$$

Short answer

The slope of the line is -3 and the y-intercept is 7.

Step-by-step solution

Rewrite equation in slope-intercept form (y = mx + c)

We start by expressing the given equation \(6 x+2 y=14\) in slope-intercept form. We subtract 6x from each side to isolate terms containing \(y\) on one side and then divide each side by 2 to get \(y\). This gives us: \(y = -3x + 7\)

Determine the slope (m)

In the slope-intercept form \(y = mx + c\), \(m\) is the slope. Looking at the equation \(y = -3x + 7\), the slope \(m\) is -3.

Determine the y-intercept (c)

In the slope-intercept form \(y = mx + c\), \(c\) is the y-intercept. Looking at the equation \(y = -3x + 7\), the y-intercept \(c\) is 7.