How do you write an equation of a line with point (6,4), slope -3/4?

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Answer 1 · 2017-02-10T12:40:16

$(y - color(red)(4)) = color(blue)(-3/4)(x - color(red)(6))$

Or

$y = color(red)(-3/4)x + color(blue)(34/4)$

The point-slope formula states: $(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))$

Where $color(blue)(m)$ is the slope and $color(red)(((x_1, y_1)))$ is a point the line passes through.

Substituting the point and the slope from the problem gives:

$(y - color(red)(4)) = color(blue)(-3/4)(x - color(red)(6))$

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

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

We can solve the equation above for $y$ to put it into this form.

$y - color(red)(4) = (color(blue)(-3/4) xx x) - (color(blue)(-3/4) xx color(red)(6))$

$y - color(red)(4) = -3/4x + 18/4$

$y - color(red)(4) + 4 = -3/4x + 18/4 + 4$

$y - 0 = -3/4x + 18/4 + (4/4 xx 4)$

$y = -3/4x + 18/4 + 16/4$

$y = -3/4x + 34/4$