What is the slope intercept form of the line with a slope of -7/2  that passes through  (1,6) ?

Jun 9, 2016

The equation of the line in slope-intercept form is

$y = - \frac{7}{2} x + 9 \frac{1}{2}$

Explanation:

The slope intercept form of a line is $y = m x + b$

For this problem we are given the slope as $- \frac{7}{2}$ and a point on the line of $\left(1 , 6\right)$

$m = - \frac{7}{2}$
$x = 1$
$y = 6$

We plug in the values and then solve for the $b$ term which is the
y-intercept.

$6 = - \frac{7}{2} \left(1\right) + b$

$6 = - 3 \frac{1}{2} + b$

Now isolate the $b$ term.

$6 + 3 \frac{1}{2} = \cancel{- 3 \frac{1}{2}} \cancel{+ 3 \frac{1}{2}} + b$

$b = 9 \frac{1}{2}$

The equation of the line in slope-intercept form becomes

$y = - \frac{7}{2} x + 9 \frac{1}{2}$