Write+equations+of+lines+when+given+two+points+&+Write+equations+of+lines+from+a+graph

=Write Equations of lines when given two points & Write equations of lines from a graph= =Abby G, Anna M, Sarah K, Sibel A.= =Period - 4=

y- intercept line crosses x- axis
Slope when Given two points :

Point-Slope Equation:  for a given point (X1, Y1) and slope m; ( Y  - Y1) = m( X  - X1) leave alone

EX:  Write the equation of a line passing through the point (3, 7) that is parallel to the line that equals y = 5x + 6 M = 5 because if a line is parallel to a line the two lines have the same slope
 * = (Y - Y1) = m(X - X1) ||
 * = (Y - 7) = 5(X - 3) ||
 * = y - 7 = 5x -15 ||
 * = y = 5x - 8 ||

Problems:


 * 1) What is the slope of the line for the points (2, 3) and (9, 6)? What is the equation of the line for point (9, 6)?
 * 2) What is the slope of the line for the points (3, 2) and (2, 3)? What is the equation of the line for point (3, 3)?
 * 3) What is the slope of the line for the points ( 5, 0) and (4, 1)? What is the equation of the line for point ( 3, 7)?

Answers: 2 Explanations:
 * 1) Using the slope formula the slope of a line can be determined using two different points, in the slope formula Y2 subtracted from Y1 is over X2 subtracted from X1. The answer is the slope of the two points, in this case the slope is 3/7. The slope can then be applied to the Point-Slope Equation, (Y - Y1) = m(X - X1) along with one of the points to determine the equation of the line, in this problem the equation for the point (9, 6) is asked for. The X and Y of the point and the slope is then plugged into the equation making the equation be; (y - 6) = 3/7(x - 9). From there the equation is worked like a problem. 3/7 is multiplied with x and -9 to get 3/7x -27/7 and 6 is added to -27/7, making the equation of the line be y = 3/7x - 69/7.

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** Point-Slope Equation of a Line ** //y// – //y// 1 = //m//(//x// – //x// 1 ), where //m// is the slope and (//x// 1, //y// 1 ) is a point on the line. Point-slope is the form used most often when finding the equation of a line.

Problem- 1. **Find the equation of the line that passes through the points (–2, 4) and (1, 2). **

Answer- 1.

Now I have the slope and //two// points. I know I can find the equation (by solving first for " // b // ") if I have a point and the slope. So I need to pick one of the points (it doesn't matter which one), and use it to solve for // b. // Using the point (–2, 4), I get: //y = mx// + //b// 4 = (– 2/3)(–2) + //b// 4 = 4/3 + //b// 4 – 4/3 = //b// 12/3 – 4/3 = //b// //b// = 8/3 ...so //y// = ( – 2/3 ) //x// + 8/3. .

**__ RISE __** ** RUN ** [] ^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ <span style="font-family: 'Vani','sans-serif'; margin: 0in 0in 6pt;">This is called rise over run. Rise is the vertical area between one point to another. The run point is the horizontal spaces between one point and the other run. You put the number of the rise over the number of the run. In the picture above the equation would be 2/2. That would then equal 1.

<span style="color: #0000ff; font-family: AHJ Latino,serif; font-size: 16pt; margin-bottom: 0in;">**3.5 Write and Graph Equations of Lines** <span style="color: #0000ff; font-family: AHJ Latino,serif; margin-bottom: 0in;">- y and x ---> leave alone, y1 and x1 ---> point that is along the line
 * 1) <span style="color: #0000ff; font-family: AHJ Latino,serif; margin-bottom: 0in;">Slope for two given points (x1, y1) and (x2, y2); m = y2-y1/x2-x1
 * 2) <span style="color: #0000ff; font-family: AHJ Latino,serif; margin-bottom: 0in;">Slope Intercept Equation: y = mx + b; y and x- leave alone, m- slope, b- y intercept
 * 3) <span style="color: #0000ff; font-family: AHJ Latino,serif; margin-bottom: 0in;">Point-Slope Equation: for a given point, (x1, y1) and slope, m; (y-y1) = m (x-x1)

<span style="color: #0000ff; font-family: AHJ Latino,serif; margin-bottom: 0in;">**RISE/RUN = SLOPE**

<span style="color: #0000ff; font-family: AHJ Latino,serif; font-weight: normal; margin-bottom: 0in;">Ex: Write an equation of the line passing through the point (17, -6) that is parallel to the line with the equation y = -2x+5

<span style="color: #0000ff; font-family: AHJ Latino,serif; font-weight: normal; margin-bottom: 0in;">Answer: (y+6) = -2(x-17) <span style="color: #0000ff; font-family: AHJ Latino,serif; font-weight: normal; margin-bottom: 0in;">y+6 = -2x+34 <span style="color: #0000ff; font-family: AHJ Latino,serif; font-weight: normal; margin-bottom: 0in;">y = -2x+28, this is according to the point-slope equation given above, (just use the same slope for parallel lines).

<span style="color: #0000ff; font-family: AHJ Latino,serif; font-weight: normal; margin-bottom: 0in;">Ex: Write an equation of the line passing through point (-14, 5) that is perpendicular to the line with the equation y = -3/2x-13/2

<span style="color: #0000ff; font-family: AHJ Latino,serif; font-weight: normal; margin-bottom: 0in;">Answer: (y-5) = 2/3(x+14) <span style="color: #0000ff; font-family: AHJ Latino,serif; font-weight: normal; margin-bottom: 0in;">y-5 = 2/3x+28/3 <span style="color: #0000ff; font-family: AHJ Latino,serif; font-weight: normal; margin-bottom: 0in;">y = 2/3x+14, this is according to the point-slope equation given above, (just use the opposite slope and negate it).

<span style="color: #0000ff; font-family: AHJ Latino,serif; font-weight: normal; margin-bottom: 0in;">Ex: Write an equation for the line drawn.

<span style="color: #0000ff; font-family: AHJ Latino,serif; font-style: normal; font-weight: normal; margin-bottom: 0in;"> <span style="color: #0000ff; font-family: AHJ Latino,serif; font-style: normal; font-weight: normal; margin-bottom: 0in;">Answer: y = 2/3x + 11/2, because the y intercept is 5 and ½ (11/2) and the slope is 2/3