How do you write an equation of a line with point (4,2), slope 1/2?

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Answer 1 · 2017-01-17T12:49:17

See the entire process for writing the equation below:

We can use the point-slope formula to write an equation for this line.

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 values from the problem gives:

$(y - color(red)(2)) = color(blue)(1/2)(x - color(red)(4))$

We can solve this for the more familiar slope-intercept form by solving for $y$ :

$y - color(red)(2) = (color(blue)(1/2) xx x) - (color(blue)(1/2) xx color(red)(4))$

$y - color(red)(2) = 1/2x - 2$

$y - color(red)(2) + 2 = 1/2x - 2 + 2$

$y - 0 = 1/2x - 0$

$y = 1/2x$