Given Two Points Writing the Equation of a Line

Equations of lines

Given two points writing the equation of a line

Slope intercept

Point Slope of a line

1. Find the slope

2. Calculate the y-int

Substitute in the slope and one set of ordered pairs (x,y) you should them be able to solve for b

3. Write the equation of a line

Parallel Lines - slopes are the same need to calculate a new y-int

Sub in same slope, sub in different x and y values and solve for new b

Perpendicular lines - slopes are opposite reciprocals, which means flip the fraction and change the sign to the opposite of what the original equation was

Perpendicular lines can have the same y-int, but you need to calculate it like all the other equations

Zero slope is a slope when the rise of the line is zero

Lines with a zero slope are horizontal

y=number

Undefined slope is a slope when the run is zero

Lines with an undefined slope are vertical

x=number

Given the following ordered pairs find the equation of the line.

(2, -5) and ( -4,7)

Given the following equation of the line find the following:

(solve the equation for y to find the slope)

1. Equation of a line parallel and through (-2,2)

Use slope and point to find b

2. Equation of a line perpendicular and through (3,-1)

Parallel Lines and Transversals

If they state lines are parallel then certain angle relationships are congruent or supplementary

Corresponding Angles - congruent

1 and 52 and 63 and 7

110 and 4

Alternate Interior Angles - congruent

3 and 52 and 4

Alternate Exterior Angles - congruent

1 and 7110 and 6

Same Side Interior Angles - supplementary

3 and 42 and 5

Knowing Shapes and what markings mean

Study the figure below. Jose believes that all of the statements about this figure must be true. Is Jose Correct? Explain why or why not for each statement.

Statement A: The figure is a quadrilateral.

Statement B: The figure is a parallelogram.

Statement C: The figure is a rectangle.

Statement D: The figure is a rhombus.

Statement E: The figure is a square.

Finding angle measure

Constructions

Part A: On your grid, draw the triangle J’K’L’, the image of triangle JKL after it has been reflected over the y-axis. Be sure to label your vertices

Part B: On your grid, draw the triangle J’’K’’L’’, the image of J’K’L’ after it has been reflected over the line y=x. Be sure to label your vertices

Construct Altitude from one vertex and median from another

Proofs - given 2 triangles congruent prove other triangles or parts congruent.

Given statements first

need 3 parts stated congruent

triangles

CPCTC

Given: