How do you write an equation of a line with point (2,-3), slope 2/3?

Question

Eva Abramson · Accepted Answer

See a solution process below:

We can use the point-slope formula for writing the equation for the line in the problem. The point-slope form of a linear equation is: #(y - color(blue)(y_1)) = color(red)(m)(x - color(blue)(x_1))# Where #(color(blue)(x_1), color(blue)(y_1))# is a point on the line and #color(red)(m)# is the slope. Substituting the slope and values from the point in the problem gives: #(y - color(blue)(-3)) = color(red)(2/3)(x - color(blue)(2))# #(y + color(blue)(3)) = color(red)(2/3)(x - color(blue)(2))# We can solve this equation for #y# to put the equation in slope-intercept format. 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(blue)(3) = (color(red)(2/3) xx x) - (color(red)(2/3) xx color(blue)(2))# #y + color(blue)(3) = color(red)(2/3)x - 4/3# #y + color(blue)(3) - 3 = color(red)(2/3)x - 4/3 - 3# #y + 0 = color(red)(2/3)x - 4/3 - (3/3 xx 3)# #y = color(red)(2/3)x - 4/3 - 9/3# #y = color(red)(2/3)x - color(blue)(13/3)#

Isaiah Anthony · Answer

undefined The equation of a line using the point-slope form is $ y - y_1 = m(x - x_1) $, where $ m $ is the slope and $ (x_1, y_1) $ is the given point. Substituting $ x_1 = 2 $, $ y_1 = -3 $, and $ m = \frac{2}{3} $ into the formula gives $ y - (-3) = \frac{2}{3}(x - 2) $. Simplifying this equation yields $ y + 3 = \frac{2}{3}(x - 2) $.