We can use the point-slope formula to solve this problem.
We first use the slope formula which requires 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 points given in the problem produces:
#m = (color(red)(-10) - color(blue)(-5))/(color(red)(-8) - color(blue)(-4))#
#m = (color(red)(-10) + color(blue)(5))/(color(red)(-8) + color(blue)(4))#
#m = (-5)/-4#
#m = 5/4#
Now with the slope and using either point from the problem we can use the point-slope formula to find the equation of 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 one of the points gives:
#(y - color(red)(-5)) = color(blue)(5/4)(x - color(red)(-4))#
#(y + color(red)(5)) = color(blue)(5/4)(x + color(red)(4))#
Solving for #y# will put this into the more familiar slope-intercept form:
#y + color(red)(5) = color(blue)(5/4)x + (color(blue)(5/4) xx color(red)(4))#
#y + color(red)(5) = color(blue)(5/4)x + 5#
#y + color(red)(5) - 5 = color(blue)(5/4)x + 5 - 5#
#y + 0 = color(blue)(5/4)x + 0#
#y = color(blue)(5/4)x#
