First, determine the slope of the line. 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)(4) - color(blue)(-4))/(color(red)(1) - color(blue)(-1)) = (color(red)(4) + color(blue)(4))/(color(red)(1) + color(blue)(1)) = 8/2 = 4#
Now, use the point-slope formula to write an equation. 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 calculated slope and the values from the first point in the problem gives:
#(y - color(red)(-4)) = color(blue)(4)(x - color(red)(-1))#
Solution 1) #(y + color(red)(4)) = color(blue)(4)(x + color(red)(1))#
You can also substitute the calculated slope and the values from the second point in the problem giving:
Solution 2) #(y - color(red)(4)) = color(blue)(4)(x - color(red)(1))#
You can also solve this equation for #y# to put the equation in slope-intercept form. 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.
#y - color(red)(4) = (color(blue)(4) * x) - (color(blue)(4) * color(red)(1))#
#y - color(red)(4) = 4x - 4#
#y - color(red)(4) + 4 = 4x - 4 + 4#
#y - 0 = 4x - 0#
Solution 3) #y = color(red)(4)x + color(blue)(0)#
Or
Solution 4) #y = color(red)(4)x#
