How do you find an equation of the line containing the given pair of points (-7, -4) and ( -2, -6)?

First, we need to determine the slope of the line running through the two points. The slope can be found by using the formula: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))#

Where #m# is the slope and (#color(blue)(x_1, y_1)#) and (#color(red)(x_2, y_2)#) are the two points on the line.

Substituting the values from the points in the problem gives:

#m = (color(red)(-6) - color(blue)(-4))/(color(red)(-2) - color(blue)(-7)) = (color(red)(-6) + color(blue)(4))/(color(red)(-2) + color(blue)(7)) = (-2)/5 = -2/5#

We can now use the point-slope formula to write and equation for the line. 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 we calculated and the values from the first point in the problem gives:

#(y - color(red)(-4)) = color(blue)(-2/5)(x - color(red)(-7))#

#(y + color(red)(4)) = color(blue)(-2/5)(x + color(red)(7))#

We can also substitute the slope we calculated and the values from the second point in the problem giving:

#(y - color(red)(-6)) = color(blue)(-2/5)(x - color(red)(-2))#

#(y + color(red)(6)) = color(blue)(-2/5)(x + color(red)(2))#

First find the slope , #m# of the line, using the two points.

#m=(y_2-y_1)/(x_2-x_1)#

Either point can be 1 or 2. I'm going by the order listed in the question. Point 1#=##(-7,-4)#, Point 2#=##(-2,-6)#

Insert the points into the equation.

#m=(-6-(-4))/(-2-(-7))=-2/5#

Now use the point slope form for a straight line.

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

Insert either point as #(x_1,y_1)#. I'm going to use Point 1 from the first part of this answer: #(-4,-7)#.

#y-(-4)=-2/5(x-(-7))#

Simplify.

#y+4=-2/5(x+7)#

#y+4=-2/5x-14#

Solve for #y# to get the slope intercept form for a straight line: #y=mx+b#, where #m# is the slope and #b# is the y-intercept.

Subtract #4# from both sides and simplify.

#y+4=-2/5x-14#

#y=-2/5x-14-4#

#y=-2/5x-18# graph{y=-2/5x-18 [-16.42, 15.6, -25.96, -9.94]}