Question

How do you write an equation in point-slope form for the given (2, 2), (-1, 4)?

Answer 1

Hint: Use equation of line for two points $(x_1, y_1)$ and $(x_2, y_2)$ and calculate slope using slope formula.

Complete step by step solution:
Given two points – (2, 2) and (-1, 4)
The slope can be calculated as m = \[\dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\]
Now let’s put the value given in formula:
$({x_1} - {y_1})$ = (2, 2)
\[({x_2} - {y_2})\] = (-1, 4)
By putting the above values in the formula,
m = $\dfrac{{4 - 2}}{{ - 1 - 2}}$
$\Rightarrow$ m = $\dfrac{2}{{ - 3}}$
Now, using the slope form of the equation,
\[(y - {y_1})\] = m \[(x - {x_1})\]
$\Rightarrow$ \[(y - 2)\] = -$\dfrac{2}{3}$\[(x - 2)\]
This is a point slope form equation.

Note: The point slope form can also be written as
\[(y - {y_2})\] = m \[(x - {x_2})\]
Or m = \[\dfrac{{y - {y_1}}}{{x - {x_1}}}\] = \[\dfrac{{y - {y_2}}}{{x - {x_2}}}\]