Graphing Linear Equations Slope – Intercept Form

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

y - intercepts 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.

and b is the y – intercept of the line. m is the slope of the line, 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, NOTE: m is the coefficient of x and b is just a constant value.

Thus, the slope is and the y – intercept is 4. Slope – Intercept Form Using our example from before We begin solving for y by subtracting 2x from both sides to obtain, Dividing both sides by 3 gives us, THINK

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. This equation is already in slope – intercept form.Graph y = –2x + 5 Graphing y = mx + b Let's graph one! Step 1: Put equation in slope intercept form STEPS TO GRAPHING Slope = –2 means Down 2 Right 1 Down 2 Right 1

Graphing ax + by = c What about 3x + 4y = –12 ? Step 1: Put equation in slope – intercept form This means solve for y. 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 ).