# How do you write an equation of a line going through (4,-1), (6,-7)?

##### 1 Answer

#### Explanation:

The equation of a line in

#color(blue)"point-slope form"# is

#color(red)(bar(ul(|color(white)(a/a)color(black)(y-y_1=m(x-x_1))color(white)(a/a)|)))#

where m represents the slope and# (x_1,y_1)" a point on the line"# To calculate m, use the

#color(blue)"gradient formula"#

#color(red)(bar(ul(|color(white)(a/a)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(a/a)|)))#

where# (x_1,y_1)" and " (x_2,y_2)" are 2 coordinate points"# The 2 points here are (4 ,-1) and (6 ,-7)

let

# (x_1,y_1)=(4,-1)" and " (x_2,y_2)=(6,-7)#

#rArrm=(-7-(-1))/(6-4)=(-6)/2=-3# Use either of the 2 points for

# (x_1,y_1)# We now have

#m=-3" and " (x_1,y_1)=(4,-1)# Substitute these values into the point-slope equation.

#y-(-1)=-3(x-4)rArry+1=-3x+12#

#rArry=-3x+11" is the equation of the line"#