How do you write the equation of a line in slope intercept, point slope and standard form given (2,2) and (2,-3)?

Question

Genesis Allen · Accepted Answer

See a solution process below:

First, we can determine the slope of the line: 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)(2))/(color(red)(2) - color(blue)(2)) = -5/0# Because we cannot divide by #0# the slope of the line is undefined. Vertical lines by definition have an undefined slope. Vertical lines have the property of for each and every value of #y# the #x# value is the same. In this problem #x# is equal to #2# for both points. Therefore, the equation of this line is: #x = 2#

Eli Assouline · Answer

undefined To write the equation of a line:

1. **Slope-intercept form**: $ y = mx + b $
   - Calculate the slope ($ m $) using the formula: $ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} $
   - Choose one of the given points and substitute its coordinates into the equation to solve for $ b $.
   - Plug the values of $ m $ and $ b $ into the equation.

2. **Point-slope form**: $ y - y_1 = m(x - x_1) $
   - Calculate the slope ($ m $) using the formula mentioned above.
   - Choose one of the given points and substitute its coordinates into the equation.

3. **Standard form**: $ Ax + By = C $
   - Rearrange the equation in slope-intercept form: $ y = mx + b $.
   - Multiply both sides by a common denominator to clear the fraction.
   - Move all terms to one side of the equation to obtain the standard form.