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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

Linear Equations

Slope-Intercept and Standard Form

slope intercept 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 form1
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 form2
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
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 51
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 52
Could you sketch the graph?

First plot the y-intercept.

The “rise” is __.

The “run” is __.

y = 3x - 5
3x 2y 4
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
y = -3/2x + 2
  • Now graph the linear equation.
writing a 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
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 equation1
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.