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Linear Equations

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.

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Linear Equations

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  1. Linear Equations Slope-Intercept and Standard Form

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

  3. 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...

  4. 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!

  5. 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)

  6. 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!

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

  8. 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 ___.

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

  10. 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?

  11. 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!

  12. 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.

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