Question

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

Answer 1

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`.