Drill #23 Determine the value of r so that a line through the points has the given slope: 1. ( r , -1 ) , ( 2 , r ) m = 2 Identify the three forms (Point.

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Drill #23 Determine the value of r so that a line through the points has the given slope: 1. ( r , -1 ) , ( 2 , r ) m = 2 Identify the three forms (Point Slope, Slope-Intercept, and Standard) of each of the following): 2. Slope = -½, passing through (0, -4) 3. Passing through the points (2, 3) and (1, -4) 4. Passing through the points (-4, 7) and (1, 8)

Drill #13 Determine the value of r so that a line through the points has the given slope: 1. ( 2 , r ) , ( -1 , 2 ) m = ½ (hint: use the slope formula) Identify the three forms (Point Slope, Slope-Intercept, and Standard) of each of the following): 2. Slope = -½, passing through (0, -4) 3. Passing through the points (2, 3) and (1, -4) 4. Find the lines parallel and perpendicular to the line 2x + y = 4 passing through (2, 1) (sketch a graph of #4)

2-4 Writing Linear Equations Objective: To write an equation of a line in slope intercept form given the slope and one or two points, and to write an equation of a line that is parallel or perpendicular to the graph of a given equation. Homework: 2-4 Study Guide (#1-8)

Slope-Intercept Form* Definition: An equation in the form of y = mx + b where m = slope and b = y- intercept In order to write an equation in slope-intercept form you need to know the slope (m) and the y- intercept (b)

Slope and y-intercept Find the equation of the line with given slope and y- intercepts: A. m = 5, b = ¾ B. m = b = C. m = 0 b = 0

Slope and a Point: Two methods Find the slope-intercept form of a line that has a slope of and passes through (-6, 1). m = ? b = ? Substitute m into the equation y = mx + b. Substitute (-6, 1) for x and y in the equation. Solve for b. Once you know m and b you can put the equation in slope-intercept form.

Point Slope Form*: Method2 Definition: An equation in the form of where Are the coordinates of a point on the line and m is the slope of the line. NOTE: For point slope form we need a point and the slope (or two points).

Slope and a point Find the slope-intercept form of the equation of the line with the given line passing through the point: A. m = 5, b = (0, -3) B. m = b = (-1, 5) C. m = ¾ b = (-4, -2)

Two Points Find the equation of the line (in slope-intercept form) passing through the points: A. (1, 5) and (2, -3) B. (-2, -5) and (1, 4)

Parallel and Perpendicular Lines Parallel Lines: In a plane, non-vertical lines with the same slope are parallel. Perpendicular Lines: In a plane, two oblique lines are perpendicular if and only if the product of their slopes is -1. Writing Equations: Parallel: Use the Same Slope Perpendicular: Use the Negative Reciprocal Slope

Writing Equations of Lines 1st Determine the slope of the line that we are writing the equation for. If finding a parallel line use the same slope If finding a perpendicular line use the negative reciprocal slope 2nd Find a point, any ordered pair (x, y) on the line. 3rd Determine what form you are going to use If Slope- Intercept, substitute the slope for m and the point (x, y) for x and y into the equation y = mx + b and solve for b If Point-Slope substitute the point and the slope m into the Point- Slope equation

Find the Equation of the Line That passes through (4, 2) and is a.) parallel to the line y = 2x – 3 b.) perpendicular to the line y = 2x – 3 Write the equations in all three forms. Graph each line (including the original)

Find the Equation of the Line That passes through (-9, 5) and is a.) parallel to the line y = -3x + 2 b.) perpendicular to the line y = -3x + 2 Write the equations in all three forms. Graph each line (including the original)