First, we need to 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)(9) - color(blue)(3))/(color(red)(2) - color(blue)(-1)) = (color(red)(9) - color(blue)(3))/(color(red)(2) + color(blue)(1)) = 6/3 = 2#
Now, we can use the point-slope formula to write an 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)(3)) = color(blue)(2)(x - color(red)(-1))#
#(y - color(red)(3)) = color(blue)(2)(x + color(red)(1))#
We can also substitute the slope we calculated and the values from the second point in the problem giving:
#(y - color(red)(9)) = color(blue)(2)(x - color(red)(2))#
If necessary, we can convert this equation to the slope-intercept form by solving for #y#. 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)(9) = (color(blue)(2) xx x) - (color(blue)(2) xx color(red)(2))#
#y - color(red)(9) = 2x - 4#
#y - color(red)(9) + 9 = 2x - 4 + 9#
#y -0 = 2x + 5#
#y = color(red)(2)x + color(blue)(5)#
