# Graphing Linear Equations Slope Intercept Form Graphing linear

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Graphing Linear Equations Slope – Intercept Form

Graphing linear Equations-EASY!!. To graph linear equations we need two pieces of information: 1) Where the line crosses the y-axis (called the y -intercept). This gives us our starting point. 2) The gradient (steepness) of the line. This tells us how many units to count up or down from the y-intercept = (rise) and how many to count to the right = (run)

Slope The slope of a line is the change in y – values divided by the change in x – values for any two points on the line. y Down 4 Rise = – 4 Right 6 The above equation takes other forms, such as Run = 6 Find the. Pick change anyintwo yx – values (RUN)points on the line (RISE) where (x 1 , y 1) and (x 2 , y 2) are any two points on the line. Slope is On a graph, the slope can also be thought of as x

y - intercepts y The y – intercept is the y – value when x = 0. When using a graph, the y – intercept is where the graph crosses the y – axis. The y – intercept of the line to the right is … y – intercept is 4. x

Slope – Intercept Form If you solve a linear equation for y, you will have put the equation in slope – intercept form. Slope intercept form is where (x , y) are again ordered pairs that make the equation true, m is the slope of the line, and b is the y – intercept of the line. NOTE: m is the coefficient of x and b is just a constant value.

Slope – Intercept Form Using our example from before We begin solving for y by subtracting 2 x from both sides to obtain, Dividing both sides by 3 gives us, Thus, the slope is THINK and the y – intercept is 4 REMEMBER: If it a positive gradient count up and if negative count down

Graphing y = mx + b Remember: If you have a whole number gradient it’s run is ALWAYS 1 Let's graph one! y STEPS TO GRAPHING Down 2 Right 1 Step 1: Put equation in slope intercept form Down 2 Right 1 Step 2: Plot the y –intercept on the graph Step 3: Starting at the y – intercept, use the slope to find other points, then connect the points. Graph y = – 2 x + 5 Slope = – 2 means This equation is already in slope – intercept form. x

Graphing ax + by = c What about 3 x + 4 y = – 12 ? y Step 1: Put equation in slope – intercept form This means solve for y. x Step 2: Plot the y – intercept. Step 3: Starting at the y – intercept, use the slope to find other points. A slope of means Down 3, Right 4…or…Up 3, Left 4 (the 3 or 4 can be negative, but not both).