How do you find the equation in slope - intercept form, of the line passing through: (-1,-1) slope = 4?

Question

How do you find the equation in slope - intercept form, of the line passing through: (-1,-1)  slope = 4?

Julia Adams · Accepted Answer

See the entire solution process below:

First, using the information in the problem write the equation in point-slope form. 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 from the problem gives: #(y - color(red)(-1)) = color(blue)(4)(x - color(red)(-1))# #(y + color(red)(1)) = color(blue)(4)(x + color(red)(1))# Now, we solve for #y# to transform the equation to 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)(1) = color(blue)(4)(x + color(red)(1))# #y + color(red)(1) = (color(blue)(4) xx x) + (color(blue)(4) xx color(red)(1))# #y + color(red)(1) = 4x + 4# #y + color(red)(1) - 1 = 4x + 4 - 1# #y + 0 = 4x + 3# #y = color(red)(4)x + color(blue)(3)#

Julia Adams · Answer

undefined The equation of the line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Given the slope (m = 4) and a point (-1, -1), substitute these values into the equation and solve for b:

y = 4x + b
-1 = 4(-1) + b
-1 = -4 + b
b = -1 + 4
b = 3

So, the equation of the line passing through (-1, -1) with a slope of 4 is y = 4x + 3.