Graphing Linear Equations, Point- Slope Form, and Parallel/Perpendicular lines REVIEW Algebra Honors Mr Smith.

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Presentation transcript:

Graphing Linear Equations, Point- Slope Form, and Parallel/Perpendicular lines REVIEW Algebra Honors Mr Smith

Objective By the end of this lesson you should be able to take given points or slope and graph and write it in point-slope, slope- intercept, and standard forms. By the end of this lesson you should be able to write equations for parallel and perpendicular lines.

Slope- Intercept form To _______, it is best to have the linear equation in slope-intercept form. Slope intercept form is y = ___ + ___ The 4 variables and definitions of slope int form are: ___ = ___________ = ________ Pause!

Slope- Intercept form To _Graph_, it is best to have the linear equation in slope-intercept form. Slope intercept form is y = mx + b The 4 variables and definitions of slope int form are: _y_ = total_m_ = slope_ x = units_b = y - intercept

Writing in slope- intercept Slope = 5, y-int = -7 4x + 3y = 18(-4, 6) (3, -8) Pause!

Writing and Graphing in slope- intercept form

Graphing For the following, the first slide is the problem, the second is the solution The first step, which we just did, is to put the info into slope-int form, and then graph.

Now, Graph y = 5x - 7

Graph y = 5x - 7

Graph y=-2x-2

Now, Graph y=-2x-2

Point-Slope Form You can write the equation of a line using point slope form, even if you do not know the second point on a line.

Write in point-slope y – y 1 = m (x – x 1 ) A line passing through point (4, -5) with a slope of -2 Pause!

Write in point-slope y – y 1 = m (x – x 1 ) A line passing through point (4, -5) with a slope of -2 y + 5 = -2 (x – 4) Next, write this in slope- int, and then standard form Pause!

To slope – intTo standard y + 5 = -2 (x – 4)y = -2x + 3 y + 5 = -2x x +2x x + y = 3 y = -2x + 3

Write in point-slope y – y 1 = m (x – x 1 ) A line passing through (3, -4) and (-6, -1) Pause!

Write in point-slope y – y 1 = m (x – x 1 ) Pause!

To slope – intTo standard

Parallel and Perpendicular

Write the equation of a line that is… Parallel to y = 5x + 6, and goes through (-5, 9) Slope is the same, so m=5, solve for b: y = mx+b > 9 = 5(-5) + b 9 = b = b, so … y = 5x + 34 is the answer

Write the equation of a line that is…

Things to Remember To Graph, you should use slope-intercept form. Start at the y-intercept, and then plot the slope from there. Moving between forms really comes down to moving terms around, and watching your signs. Parallel lines have the same slope, perpendicular lines are opposite reciprocals.