How do you find the Slope, Y-intercept and X-intercept of the Line x-3y+7=0?

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Answer 1 · 2017-01-14T20:32:35

See the entire process for answering these questions below:

First, to find the slope and y-intercept we can convert this equation into the slope-intercept form by solving for $y$ $y$ .

The slope-intercept form of a linear equation is:

$y = m x + b$ $y = color(red)(m)x + color(blue)(b)$

Where $m$ $color(red)(m)$ is the slope and $b$ $color(blue)(b$ is the y-intercept value.

$x - 3 y + 7 + 3 y = 0 + 3 y$ $x - 3y + 7 + color(red)(3y) = 0 + color(red)(3y)$

$x - 3 y + 3 y + 7 = 3 y$ $x - 3y + color(red)(3y) + 7 = color(red)(3y)$

$x - 0 + 7 = 3 y$ $x - 0 + 7 = color(red)(3y)$

$x + 7 = 3 y$ $x + 7 = 3y$

or

$3 y = x + 7$ $3y = x + 7$

$\frac{3 y}{3} = \frac{x + 7}{3}$ $(3y)/color(red)(3) = (x + 7)/color(red)(3)$

$(color(red)(cancel(color(black)(3)))y)/cancel(color(red)(3)) = x/3 + 7/3$

$y = 1/3x + 7/3$

Therefore:

The slope is $color(red)(m = 1/3)$

The y-intercept is $color(blue)(b = 7/3)$ or (0, 7/3)

To find the x-intercept we set $y = 0$ and solve for $x$ :

$0 = 1/3x + 7/3$

$0 - color(red)(7/3) = 1/3x + 7/3 - color(red)(7/3)$

$-7/3 = 1/3x + 0$

$-7/3 = 1/3x$

$color(red)(3) xx -7/3 = color(red)(3) xx 1/3x$

$cancel(color(red)(3)) xx -7/color(red)(cancel(color(black)(3))) = cancel(color(red)(3)) xx 1/color(red)(cancel(color(black)(3)))x$

$-7 = x$ or $x = -7$

Therefore:

The x-intercept is $color(green)(x = -7)$ or (-7, 0)