How do you write the slope intercept form of a line with slope 5/2 passing through (-7,3)?

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How do you write the slope intercept form of a line with slope 5/2 passing through (-7,3)?

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Answer 1 · 2016-12-20T12:20:05

$y = \frac{5}{2} x + \frac{41}{2}$ $y = 5/2x + 41/2$

Explanation:

First, build the equation using the information given, the slope and a point, using the point-slope formula.

The point-slope formula states: $(y - y_{1}) = m (x - x_{1})$ $color(red)((y - y_1) = m(x - x_1))$
Where $m$ $color(red)(m)$ is the slope and $color(red)(((x_1, y_1)))$ is a point the line passes through.

Substituting the information from the problem gives the equation:

$y - 3 = 5/2(x - -7)$

$y - 3 = 5/2(x + 7)$

The slope-intercept for of a linear equation is $color(red)(y = mx + b)$ where $color(red)(m)$ is the slope and $color(red)(b)$ is the y-intercept.

To transform our equation we must solve for $y$ while keeping the equation balanced:

$y - 3 = 5/2x + (5/2 xx 7)$

$y - 3 = 5/2x + 35/2$

$y - 3 + color(red)(3) = 5/2x + 35/2 + color(red)(3)$

$y - 0 = 5/2x + 35/2 + (3 xx 2/2)$

$y = 5/2x + 35/2 + 6/2$

$y = 5/2x + (35 + 6)/2$

$y = 5/2x + 41/2$

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How do you write the slope intercept form of a line with slope 5/2 passing through (-7,3)?

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