How do you write an equation of a line with point (2,6), slope 2?

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Answer 1 · 2017-01-18T15:03:47

See the entire solution process below:

To write this equation we can use the point-slope formula.

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 this equation:

$(y - color(red)(6)) = color(blue)(2)(x - color(red)(2))$

We can also solve for $y$ to put this equation into the more familiar slope-intercept form:

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.

$y - color(red)(6) = (color(blue)(2) xx x) - (color(blue)(2) xx color(red)(2))$

$y - color(red)(6) = 2x - 4$

$y - color(red)(6) + 6 = 2x - 4 + 6$

$y - 0 = 2x + 2$

$y = 2x + 2$