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

1 Answer
Johnson Z.
Mar 31, 2016

#y=7/5x-6#

Explanation:

Recall that the general formula for a line in slope-intercept form is:

#color(blue)(|bar(ul(color(white)(a/a)y=mx+bcolor(white)(a/a)|)))#

where:
#y=#y-coordinate
#m=#slope
#x=#x-coordinate
#b=#y-intercept

Determining the Equation of the Line
#1#. Start by determining the slope between the two points using the slope formula. When determining the slope, either #(5,1)# or #(0,-6)# can be coordinate #1# or #2#.

As long as you do the calculations correctly, it doesn't matter which one you choose. In this case, we will let coordinate #1# be #(5,1)# and coordinate #2# be #(0,-6)#.

#m=(y_2-y_1)/(x_2-x_1)#

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

#m=(-7)/(-5)#

#m=7/5#

#2#. Substitute #m=7/5# into #y=mx+b#. Choose either coordinate #1# or #2# into substitute into the equation. In this case, we will choose coordinate #1#. Then solve for #b#.

#y=7/5x+b#

#1=7/5(5)+b#

#1=7+b#

#b=-6#

#3#. Write out the equation.

#color(green)(|bar(ul(color(white)(a/a)y=7/5x-6color(white)(a/a)|)))#

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