How do you find the slope and intercept to graph #2x+y=7#?

1 Answer
sente
Nov 6, 2015

Manipulate the equation into the slope-intercept form #y = mx + b# to find the slope #m =-2# and y-intercept #b=7#

Explanation:

The simplest method of finding the slope and y-intercept of a linear equation is to put it into the slope-intercept form of #y=mx+b# where #m# is the slope and #b# is the y-intercept.

Starting from #2x + y = 7#, all we need to do is subtract #2x# from each side of the equation to obtain # y = -2x + 7#

The equation is then in slope-intercept form, where #m = -2# and #b = 7#

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Let's take a look at why the y-intercept and slope are represented by #b# and #m#.

First, note that the y-intercept is the point on the graph where #x=0#
So, setting #x=0# in the equation #y=mx+b# gives #y=b#, showing that the graph intersects the y-axis at #(0, b)#.

Next, note that as #b# remains constant, if you increase the value of #x# by #1# from any initial value, the value of #y# increases by #m#. So, by the #"slope"="rise"/"run"# formula, we have a rise of #m# for a run of #1#, meaning the slope of the graph is #m/1 = m#.

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