What is the point slope form of the line that passes through (3,7) and has a slope of m=0? What about the y-intercept form?

Question

What is the point slope form of the line that passes through (3,7) and has a slope of m=0?  What about the y-intercept form?

Ethan Adkins · Accepted Answer

Point-slope form: #y-7=0(x-3)#

Slope-intercept form: #y=7# Point-slope form: #y-y_1=m(x-x_1)#, where #m# is the slope and #(x_1,y_1)# is the point. Plug in the known values. #y-7=0(x-3)# #larr# point-slope form Slope-intercept form: #y=mx+b#, where #m# is the slope and #b# is the y-intercept. Solve the point-slope form for #y#. #y-7=0(x-3)# #y-7=0# Add #7# to both sides. #y=7# #larr# slope-intercept form, where #m=0# graph{y-7=0(x-3) [-11.9, 10.6, -0.54, 10.71]}

Hazel Anglin · Answer

undefined Point-slope form: $ y - 7 = 0 \cdot (x - 3) $

Simplified: $ y - 7 = 0 $

Y-intercept form: $ y = 7 $

Avery Alexander · Answer

undefined The point-slope form of a linear equation is given by $ y - y_1 = m(x - x_1) $, where $ (x_1, y_1) $ is a point on the line and $ m $ is the slope of the line.

Given that the slope $ m = 0 $ and the point $ (3,7) $, the point-slope form becomes:

$$ y - 7 = 0(x - 3) $$

$$ y - 7 = 0 $$

$$ y = 7 $$

So, the point-slope form of the line passing through (3,7) with a slope of $ m = 0 $ is $ y = 7 $.

The y-intercept form of a linear equation is $ y = mx + b $, where $ m $ is the slope of the line and $ b $ is the y-intercept.

Given that the slope $ m = 0 $, and the line passes through the point $ (3,7) $, the y-intercept form becomes:

$$ y = 0x + b $$

$$ y = b $$

Since the line passes through the point $ (3,7) $, when $ x = 3 $, $ y = 7 $. Therefore, the y-intercept $ b $ is also 7.

So, the y-intercept form of the line passing through (3,7) with a slope of $ m = 0 $ is $ y = 7 $.