How do you write equation of a line in slope-intercept form that has a slope of -1/4 and passes through the point (8, -1)?

Question

Eva Abramson · Accepted Answer

#y = color(red)(-1/4)x + color(blue)(1)#

First, we can write an equation in point-slope form. The point-slope formula states: #(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))#

Where #color(blue)(m)# is the slope and #color(red)(((x_1, y_1)))# is a point the line passes through.

Substituting the slope and point from the problem gives:

#(y - color(red)(-1)) = color(blue)(-1/4)(x - color(red)(8))#

#(y + color(red)(1)) = color(blue)(-1/4)(x - color(red)(8))#

The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)#

Where #color(red)(m)# is the slope and #color(blue)(b)# is the y-intercept value.

We can now solve the point-slope form of the equation for #y# to put it in slope-intercept form.

#y + color(red)(1) = (color(blue)(-1/4) xx x) - (color(blue)(-1/4) xx color(red)(8))#

#y + color(red)(1) = -1/4x - (-8/4)#

#y + color(red)(1) = -1/4x + 2#

#y + color(red)(1) - 1 = -1/4x + 2 - 1#

#y + 0 = -1/4x + 1#

#y = color(red)(-1/4)x + color(blue)(1)#

Savannah Anderson · Answer

undefined The equation of the line in slope-intercept form with a slope of -1/4 and passing through the point (8, -1) is:

$$ y = -\frac{1}{4}x + \frac{5}{4} $$