What is the slope-intercept form of the line passing through # (5, 1)# and # (0, -6) #?

3 Answers
Mar 3, 2018

Answer:

The general slope intercept form of a line is

#y=mx+c#

where #m# is the slope of the line and #c# is its #y#-intercept (the point at which the line cuts the #y# axis).

Explanation:

First, get all the terms of the equation. Let us calculate the slope.

#"slope" = (y_2-y_1)/(x_2-x_1)#

# =(-6-1)/(0-5)#

# = 7/5#

The #y#-intercept of the line is already given. It is #-6# since the #x# coordinate of the line is zero when it intersects the #y# axis.

#c=-6#

Use the equation.

#y=(7/5)x-6#

Answer:

#y=1.4x+6#

Explanation:

#P-=(5,1)#
#Q-=(0,-6)#
#m=(-6-1)/(0-5)=-7/-5#
#m=1.4#
#c=1-1.4xx5=1-7#
#c=6#
#y=mx+c#
#y=1.4x+6#

Mar 3, 2018

Answer:

One answer is: #(y-1)=7/5(x-5)#
the other is: #(y + 6)=7/5(x-0)#

Explanation:

The slope-intercept form of a line tells you what you need to find first: the slope.
Find slope using #m=(y_2 - y_1)/(x_2 - x_1)#
where #(x_1,y_1)# and #(x_2,y_2)# are the given two points
#(5,1)# and #(0,-6)#:

#m=(-6-1)/(0-5) = (-7)/-5 = 7/5#

You can see this is in both answers.

Now choose either point and plug in to the slope-intercept form of a line: #(y - y_1) = m(x - x_1)#

Choosing the first point results in the first answer and choosing the second point yields the second answer. Also note that the second point is technically the y-intercept, so you could write the equation in slope-intercept form (#y=mx+b#): #y=7/5x-6#.