What is the equation in slope intercept form that passes through the point (3,9) and has a slope of -5?

2 Answers
Dec 9, 2017

#y=-5x+24#

Explanation:

Given:

Point: #(3,9)#

Slope: #-5#

First determine the point-slope form , then solve for #y# to get the slope-intercept form.

Point-slope form:

#y-y_1=m(x-x_1)#,

where:

#m# is the slope, and #(x_1,y_1)# is a point on the line.

Plug in the known values.

#y-9=-5(x-3)# #larr# Point-slope form

Slope-intercept form:

#y=mx+b#,

where:

#m# is the slope and #b# is the #y#-intercept.

Solve for #y#.

Expand the right-hand side.

#y-9=-5x+15#

Add #9# to both sides.

#y=-5x+15+9#

Simplify.

#y=-5x+24# #larr# Slope-intercept form

Dec 9, 2017

Since the slope-intercept form is #y = mx + b# and we do not know the #y#-intercept (#b#), substitute what is known (the slope and the point's coordinates), solve for #b#, then obtain #y = -5x + 24#.

Explanation:

The slope-intercept form is #y = mx + b#. First, we write down what we already know:
The slope is #m = -5#,
And there's a point #(3, 9)#.

What we do not know is the #y#-intercept, #b#.
Since every point on the line must obey the equation, we could substitute the #x# and #y# values that we already have:
#y = mx + b# becomes #9 = (-5) * 3 + b#

And then solve algebraically:
#9 = (-5) * 3 + b#
Multiply:
#9 = (-15) + b#
Add both sides by #15#:
#24 = b#
So now we know that the #y#-intercept is #24#.

Therefore, the slope-intercept form for this line is:
#y = -5x + 24#