What is the equation in point-slope form and slope intercept form for the line given slope= -1/2, (0,3)?

Question

What is the equation in point-slope form and slope intercept form for the line given  slope= -1/2, (0,3)?

Genesis Allen · Accepted Answer

See a solution process below:

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 gives: #(y - color(blue)(3)) = color(red)(-1/2)(x - color(blue)(0))# 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. #(0, 3)# is the same as having a #y#-intercept of #3# Substituting gives: #y = color(red)(-1/2)x + color(blue)(3)#

Julia Adams · Answer

undefined Point-slope form: $ y - y_1 = m(x - x_1) $
Given: $ m = -\frac{1}{2} $ and $ (x_1, y_1) = (0,3) $
Substituting into the point-slope form:
$ y - 3 = -\frac{1}{2}(x - 0) $
$ y - 3 = -\frac{1}{2}x $

Slope-intercept form: $ y = mx + b $
Given: $ m = -\frac{1}{2} $ and $ (x, y) = (0,3) $
Substituting into the slope-intercept form to find $ b $:
$ 3 = -\frac{1}{2}(0) + b $
$ 3 = b $
So, $ b = 3 $
The equation becomes:
$ y = -\frac{1}{2}x + 3 $