Graphs Using Slope-Intercept Form

Key Questions

How do you know if you graphed the linear equation correctly?

If your line goes through two distinct points of the equation, then your line is correct.

I hope that this was helpful.

Wataru · 1 · Nov 9 2014
Once you graph the y-intercept, how do you determine the second point?

You can choose any nonzero value $x_{2}$ $x_2$ for $x$ $x$ and plug it into the equation of the line you are working on to find the corresponding $y$ $y$ -coordinate $y_{2}$ $y_2$ . Your second point is $(x_{2}, y_{2})$ $(x_2,y_2)$ .

I hope that this was helpful.

Wataru · 1 · Nov 1 2014
How do you graph a line using slope-intercept form?

The equation of a line in explicit form is:

$y = m x + q$ $y=mx+q$ , where $m$ $m$ is the slope and $q$ $q$ the y-intercept.

It is easier to show the procedure with some example:

$y = 2$ $y=2$ : this line is parallel to the x-axis and it passes from the point $P (0, 2)$ $P(0,2)$ .

$x = 3$ $x=3$ : this line is parallel to the y-axis and it passes from the point $P (2, 0)$ $P(2,0)$ .

$y = x + 1$ $y=x+1$ : this line is parallel to the bisector of the I and III quadrants and it passes from the point $P (0, 1)$ $P(0,1)$ .

graph{x+1 [-10, 10, -5, 5]}

$y = - x - 1$ $y=-x-1$ : this line is parallel to the bisector of the II and IV quadrants and it passes from the point $P (0, - 1)$ $P(0,-1)$ .

graph{-x-1 [-10, 10, -5, 5]}

$y = \frac{2}{3} x + 1$ $y=2/3x+1$ : we have to find the point $P (0, 1)$ $P(0,1)$ , from this point we have to "count" 3 units to the right and then 2 units to the up, so we can find the point #Q(3,3), then we have to join the two point found.

graph{2/3x+1 [-10, 10, -5, 5]}

$y = - \frac{1}{2} x - 1$ $y=-1/2x-1$ : we have to find the point $P (0, - 1)$ $P(0,-1)$ , from this point we have to "count" 2 units to the left and then 2 units to the up, so we can find the point #Q(-2,0), then we have to join the two point found.

graph{-1/2x-1 [-10, 10, -5, 5]}

The difference in these two last examples is the "choice" of the "right" and the "left". Right, if the $m$ $m$ is positive; left, if the $m$ $m$ is negative.

Massimiliano · 1 · Jan 30 2015

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Graphs of Linear Equations and Functions

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Graphs Using Slope-Intercept Form

Key Questions

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Graphs of Linear Equations and Functions