What is the equation of the line that has slope 2/3 and passes through the point (-2,1)?

Question

Eli Assouline · Accepted Answer

#(y - 1) = 2/3(x + 2)#

or

#y = 2/3x + 7/3# To find this equation we can use the point-slope formula: 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 information we are given in the problem produces: #(y - color(red)(1)) = color(blue)(2/3)(x - color(red)(-2))# #(y - color(red)(1)) = color(blue)(2/3)(x + color(red)(2))# To put this into slope-intercept form (#y = mx + b#) we can solve for #y# as follows: #(y - color(red)(1)) = color(blue)(2/3)x + (color(blue)(2/3) xx color(red)(2))# #y - color(red)(1) = color(blue)(2/3)x + 4/3# #y - color(red)(1) + color(green)(1) = color(blue)(2/3)x + 4/3 + color(green)(1)# #y - 0 = color(blue)(2/3)x + 4/3 + (color(green)(1) xx 3/3)# #y = color(blue)(2/3)x + 4/3 + color(green)(3/3)# #y = color(blue)(2/3)x + 7/3#

Jace Anderson · Answer

undefined The equation of the line with slope $ \frac{2}{3} $ and passing through the point $(-2,1)$ is $ y - 1 = \frac{2}{3}(x + 2) $.