Linear Equations: Slope intercept and standard form

• A linear equation in an equation that forms a straight line when graphed on a coordinate plane.

• Slope Intercept Form is a type of linear equation in the form of y=mx+b, where m is the slope and b is the y-intercept.

• The y-intercept is the number in place of b in y=mx+b.

• This is the starting point when graphing a line!

• The y-intercept is where the line will cross through the y-axis on the coordinate plane.

• Pay attention to the symbol in front of b in the equation! This tells you if it is positive or negative (y=3x-4 means b= -4)

• The y-intercept written as an ordered pair is (0,b)... if b=-4, the ordered pair will be (0,-4)

• The slope is a number that tells how steep the line will be.

• Slope is the m in y=mx+b. Slope is a fraction... if the number you have is not a fraction, put a 1 under it (3 = 3/1)

• After putting the y-intercept on the graph, the slope tells you where to go next. The top number is the rise (it tells you how far to go up if its positive, or down if its negative), and the bottom number is the run (it tells you how far to go to the right)

• If slope is positive, it will go up to the right ( / ), and if slope is negative, it will go down the the right ( \ )

How to graph y=mx+b

In y=mx+b, m is the slope. Slope is the rate of change of the line, or the change in y over the change in x. We say "Rise over Run" to remember this.

In y=mx+b, b is the y-intercept, which is where the line crosses the y-axis. If you have slope-intercept form, b is always your starting point when you are graphing a line.

• step 1: plot the y-intercept

• step 2: start at y-intercept and do rise over run with slope, then plot the point

Sometimes, lines are in other forms, like standard form (for example, 6x+3y= 9). You can solve this for y to convert the equation to slope-intercept form, so you can easily graph using the slope and the y-intercept.

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(Remember literal equations? This is an application of those!)​

Ax+By = C to y=mx+b

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We will need to solve for y​ to get this in slope-intercept form so we can graph it.

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1. Move the term with no y over to the other side

2. Divide both sides by B​

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​Another way to graph standard form is to find the x- and y-intercepts.

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x-intercept is when y=0, and y-intercept is when x=0.​

• Graph your x-intercept

• Graph your y-intercept

• Draw a line connecting the 2 points