How do you find the equation in slope - intercept form, of the line passing through the points (-1, 2) and (3, -4)?

Question

Eva Adamson · Accepted Answer

See a solution process below:

First, we need to determine the slope of the line for the equation. 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)(2))/(color(red)(3) - color(blue)(-1)) = (color(red)(-4) - color(blue)(2))/(color(red)(3) + color(blue)(1)) = -6/4 = -3/2# 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. Because we have calculated the slope and the problem gives us a point from the line, we can substitute the slope we calculated for #m# and we can substitute the values from either of the points in the problem and solve for #b#: #2 = (color(red)(-3/2) xx -1) + color(blue)(b)# #2 = 3/2 + color(blue)(b)# #-color(red)(3/2) + 2 = -color(red)(3/2) + 3/2 + color(blue)(b)# #-color(red)(3/2) + (2/2 xx 2) = 0 + color(blue)(b)# #-color(red)(3/2) + 4/2 = color(blue)(b)# #1/2 = color(blue)(b)# We can now substitute the slope and #b# value we calculated into the formula to give the equation in slope-intercept form: #y = color(red)(-3/2)x + color(blue)(1/2)#

Ethan Adkins · Answer

undefined To find the equation of the line passing through two points (-1, 2) and (3, -4) in slope-intercept form (y = mx + b), follow these steps:

1. Calculate the slope (m) using the formula: m = (y2 - y1) / (x2 - x1).
2. Once you have the slope, substitute one of the points into the equation y = mx + b and solve for b.
3. Once you have the slope (m) and the y-intercept (b), plug them into the equation y = mx + b to get the final equation.