How do you write an equation in slope intercept form using the points (4,-3) , (2,3)?

1 Answer
Jan 18, 2017

y = -3x + 9

Explanation:

First, we will write and equation in point-slope form and then convert to slope-intercept form.

To use the point-slope form we must first determine the slope.

The slope can be found by using the formula: m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))

Where m is the slope and (color(blue)(x_1, y_1)) and (color(red)(x_2, y_2)) are the two points on the line.

Substituting the values from the points in the problem gives:

m = (color(red)(3) - color(blue)(-3))/(color(red)(2) - color(blue)(4))

m = (color(red)(3) + color(blue)(3))/(color(red)(2) - color(blue)(4))

m = 6/-2 = -3

We can now use this calculated slope and either point to write the equation in point-slope form.

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.

Again, substituting gives:

(y - color(red)(-3)) = color(blue)(-3)(x - color(red)(4))

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

We can now convert this to 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.

We can solve our equation for y:

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

y + color(red)(3) = (color(blue)(-3) xx x) - (color(blue)(-3) xx color(red)(4))

y + 3 = -3x - (-12)

y + 3 = -3x + 12

y + 3 - color(red)(3) = -3x + 12 - color(red)(3)

y + 0 = -3x + 9

y = -3x + 9