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4-77.

Determine the slope and $y$-intercept for each line.

There are many methods possible to accomplish this.

1) Slope and $y$-intercept can be identified from the Slope-Intercept form of the equation.
This form is often written as $y = mx + b$ where $m$ is the slope and $b$ is the $y$-intercept.

2) Alternatively, you could calculate the $y$-intercept (where $x = 0$) and calculate any other point (by letting $x = 1$ for instance) and then calculate the slope from those two coordinates.

1. $2x+7y=14$

Solving for y will place this equation in Slope-Intercept Form.

$7y=-2x + 14$

${y=\frac{-2}{7}x+2}$

${\text{The slope is }\frac{-2}{7}\text{ and the } y\text{-intercept is }(0,2)}$

1. $y=6-\frac{x}{3}$

• This equation is written in Slope-Intercept form, but it has been rearranged.
Its form is more like $y = mx + b$

${\text{Slope is -}\frac{1}{3}\text{ and the } y\text{-intercept is }(0,6)}$

1. $y=\frac{10x-2}{2}$

This equation will be easier to read if the fraction is separated into two terms.

$y=\frac{10}{2}x -\frac{2}{2}$

1. $y=3x$

See the hint for part (a).