How do you find the equation of the line with slope m=7/8 and point (1,-2)?

Question

Isaiah Anthony · Accepted Answer

#y=7/8x-23/8#

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

#color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))# where m represents the slope and # (x_1,y_1)" a point on the line".#

#"here " m=7/8" and " (x_1,y_1)=(1,-2)#

substitute these values into the equation.

#y+2=7/8(x-1)larr" in point-slope form"#

If we distribute and simplify we obtain an alternative form of the equation.

#y+2=7/8x-7/8#

#rArry=7/8x-7/8-2#

#rArry=7/8x-23/8larr" in slope-intercept form"#

Avery Alexander · Answer

undefined To find the equation of the line with slope $ m = \frac{7}{8} $ and passing through the point $ (1, -2) $, you can use the point-slope form of a linear equation:

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

Substitute the given values $ m = \frac{7}{8} $, $ x_1 = 1 $, and $ y_1 = -2 $ into the equation:

$$ y - (-2) = \frac{7}{8}(x - 1) $$

Simplify:

$$ y + 2 = \frac{7}{8}(x - 1) $$

$$ y + 2 = \frac{7}{8}x - \frac{7}{8} $$

$$ y = \frac{7}{8}x - \frac{7}{8} - 2 $$

$$ y = \frac{7}{8}x - \frac{7}{8} - \frac{16}{8} $$

$$ y = \frac{7}{8}x - \frac{23}{8} $$

So, the equation of the line is $ y = \frac{7}{8}x - \frac{23}{8} $.