What is the slope intercept form of the line passing through #(2,-3) # with a slope of #-1/2 #?

Question

What is the slope intercept form of the line passing through #(2,-3)   # with a slope of #-1/2 #?

Nathan Axel · Accepted Answer

#y=-1/2x-2#

The equation of a line in #color(blue)"slope-intercept form"# is

#color(red)(bar(ul(|color(white)(a/a)color(black)(y=mx+b)color(white)(a/a)|)))# where m represents the slope and b, the y-intercept.

here the slope #=-1/2# so we can write the partial equation as

#y=-1/2x+b#

To find b, substitute the coordinates of the point (2 ,-3) into the partial equation.

#rArr(-1/2xx2)+b=-3#

#rArr-1+b=-3rArrb=-3+1=-2#

#rArry=-1/2x-2" is equation in slope-intercept form"#

Eva Adamson · Answer

undefined The slope-intercept form of a line is given by the equation $ y = mx + b $, where $ m $ is the slope and $ b $ is the y-intercept. Given that the slope $ m = -\frac{1}{2} $ and the point $ (2,-3) $, we can use the point-slope formula to find the equation of the line:

$$ y - y_1 = m(x - x_1) $$

Substituting the values $ x_1 = 2 $ and $ y_1 = -3 $ into the formula:

$$ y - (-3) = -\frac{1}{2}(x - 2) $$
$$ y + 3 = -\frac{1}{2}(x - 2) $$

Expanding and rearranging:

$$ y + 3 = -\frac{1}{2}x + 1 $$
$$ y = -\frac{1}{2}x + 1 - 3 $$
$$ y = -\frac{1}{2}x - 2 $$

So, the slope-intercept form of the line passing through the point $ (2,-3) $ with a slope of $ -\frac{1}{2} $ is $ y = -\frac{1}{2}x - 2 $.