What is the slope-intercept form of the line passing through (4, 5) and  (2, 2) ?

Feb 24, 2016

$y = \frac{3}{2} x - 2$
The equation for slope intercept is $y = m x + b$
For this equation the slope $m = \frac{3}{2}$
and the y intercept is $b = - 2$

Explanation:

The formula for slope is $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

For the points (4,5) and (2,2) where
${x}_{1} = 4$
${y}_{1} = 5$
${x}_{2} = 2$
${y}_{2} = 2$

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

$m = \frac{2 - 5}{2 - 4}$

$m = \frac{- 3}{-} 2$

$m = \frac{3}{2}$

To determine the equation of the line we can use the point slope formula and plug in the values given in the question.

$\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$

$m = \frac{3}{2}$
${x}_{1} = 4$
${y}_{1} = 4$

$\left(y - 4\right) = \frac{3}{2}$(x - 4)#

$y - 4 = \frac{3}{2} x - 6$

$y - 4 + 4 = \frac{3}{2} x - 6 + 4$

$y = \frac{3}{2} x - 2$

The equation for slope intercept is $y = m x + b$

For this equation the slope $m = \frac{3}{2}$
and the y intercept is $b = - 2$