Question #43077

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Answer 1 · 2017-04-27T23:23:43

See the entire solution process below:

The slope-intercept form of an equation is: $y = m x + b$ $y = color(red)(m)x + color(blue)(b)$

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

We can substitute the values of the point from the problem for $x$ $x$ and $y$ $y$ and the slope for the problem for $m$ $m$ and solve for $b$ $b$ :

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

$- 3 = (- 1 \cdot 4) + b$ $-3 = (color(red)(-1) * 4) + color(blue)(b)$

$- 3 = - 4 + b$ $-3 = -4 + color(blue)(b)$

$4 - 3 = 4 - 4 + b$ $color(red)(4) - 3 = color(red)(4) - 4 + color(blue)(b)$

$1 = 0 + b$ $1 = 0 + color(blue)(b)$

$1 = b$ $1 = color(blue)(b)$

We can now substitute the slope from the problem and the y-intercept we calculated into the slope-intercept formula to write the equation:

$y = - 1 x + 1$ $y = color(red)(-1)x + color(blue)(1)$