How do you write the equation of the line that has contains the point (5, -4) and has a slope of 5?

Question

Abigail Allen · Accepted Answer

#(y + color(red)(4)) = color(blue)(5)(x - color(red)(5))#

or

#y = color(blue)(5)x - 29# We can use the point-slope formula to determine the equation of the line in this problem. 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)(-4)) = color(blue)(5)(x - color(red)(5))# #(y + color(red)(4)) = color(blue)(5)(x - color(red)(5))# We can put this in the more familiar slope-intercept form by solving for #y#: #y + color(red)(4) = color(blue)(5)x - (color(blue)(5) xx color(red)(5))# #y + color(red)(4) = color(blue)(5)x - 25# #y + color(red)(4) - 4 = color(blue)(5)x - 25 - 4# #y + 0 = color(blue)(5)x - 29# #y = color(blue)(5)x - 29#

Julia Adams · Answer

undefined To write the equation of the line that contains the point (5, -4) and has a slope of 5, you can use the point-slope form of a linear equation:

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

Substitute the given point (5, -4) and slope m = 5 into the equation:

$$ y - (-4) = 5(x - 5) $$

$$ y + 4 = 5(x - 5) $$

$$ y + 4 = 5x - 25 $$

$$ y = 5x - 25 - 4 $$

$$ y = 5x - 29 $$

So, the equation of the line is $ y = 5x - 29 $.