Slope-Intercept and Standard Form

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Presentation transcript:

Slope-Intercept and Standard Form Linear Equations Slope-Intercept and Standard Form

Slope-Intercept Form Any linear equation can be solved for y and written like this: This form of a linear equation is called ______-_________ form.

Slope-Intercept Form The “m” represents the _____ of the line. It is often convenient to write the slope as a fraction, since slope is defined as...

Slope-Intercept Form The “b” represents the __-__________. (Which is where the line crosses the __-_____.) It is important to pay attention to the signs of both m and b!

y = 3x - 5 Can you determine the slope and the y-intercept of this equation? The slope is ___ Which we might choose to write as ___ (to make the “rise” and “run” more obvious)

y = 3x - 5 What about the y-intercept? You didn’t miss the negative sign did you? We can graph this equation by first plotting the y-intercept, then plotting a second point found via the slope!

y = 3x - 5 Could you sketch the graph? First plot the y-intercept. The “rise” is __. The “run” is __.

3x + 2y = 4 Re-write the equation in slope-intercept form. Solve for y. Put the “x” term first on the right side of the equation. The slope is ___ and the y-int is ___.

y = -3/2x + 2 Now graph the linear equation.

Writing a Linear Equation Suppose you were given a point on a line and a slope. Could you write the equation of the line? How could you find the y-intercept?

m = 2/3 and the line contains (-3,-2) Since we know the slope and at least one value of x and y that makes the equation true, we can simply substitute and solve!

Writing a Linear Equation Now we know both the slope and the y-intercept. Can you write the equation in both slope-intercept and standard form? Write the equation in slope-intercept form.