POINTS AND LINES ON THE COORDINATE PLANE

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Presentation transcript:

POINTS AND LINES ON THE COORDINATE PLANE

SLOPE OF A LINEAR FUNCTION It is always constant Rate of change of y with respect to x.

Finding Equations of Lines Given a point and a slope – Find the equation of the line given A(2, 5) on the line and that the line has a slope of -3. You can use either…. y = mx + b form or y - y1 = m(x – x1) form In the first equation m is the slope and b is the y-intercept In the 2nd equation m is the slope and (x1, y1) is a point.

Finding Equations of Lines Given a point and a slope – Find the equation of the line given A(2, 5) on the line and that the line has a slope of -3. Which do you think is a better choice? y - y1 = m(x – x1) form because you are given the slope and a point! Substitute in values: y - 5 = -3(x – 2) done!

Finding Equations of Lines Given 2 points - Find the equation of the line passing through points A(3, 6) and B(1, -5). Find slope first. Then repeat the process from the previous example! y - 6 = 5.5(x – 3)

Graphing a Line – What is the best method? y = 2x + 1 (Since this equation is in slope intercept form, use slope/intercept) y + 1 = 2(x + 1) (Use slope and point since its point/slope form) (produces the same line!) y = 2x + 2 (in slope/intercept, but y-intercept irrational substitute values to get 2 points) 2x + 4y = 5 (Find x and y intercepts x = 0  y-intercept y = 0  x-intercept)

Vertical and Horizontal Lines Horizontal lines have an equation of the form y = b where ‘b’ is the y-coordinate of any point on the line. Any horizontal line has a slope of 0. Vertical lines have an equation of the form x = a where ‘a’ is the x-coordinate of any point on the line. The slope is undefined for any vertical line.

Parallel and Perpendicular Lines the same! The slopes of parallel lines are __________. The slopes of perpendicular lines are ______________________________________. Find the equation of the line passing through (3, 1) and perpendicular to y = 4x – 2. opposite and reciprocal! y - 1= -.25(x – 3)

perpendicular vertical collinear horizontal parallel reciprocal slope intercept linear