Writing an equation of a line

YOUR GOAL : To write an equation of

line.WHAT IS NEEDED: The slope and the y-intercept.

An equation consists of….y = mx + b

Slope

Y-intercept

Writing the equation: given the slope and y-intercept.

Using the slope-intercept form of a line

y= mx + b1.Plug in m(the slope) 2. Plug in b(the y-intercept).

Presto, you have just written the equation of a

line!

Example 1 Example: Write an equation for a line

that has slope of -1/2 and a y-intercept of 3.

y = mx + b1.Plug in m (the slope). y = -1/2x +

b2. Plug in b (the y-intercept).y = -1/2x + 3

Done!

Writing the equation: given the slope and a point

Using the slope-intercept form of a line

y= mx + b1.Plug in m and plug in the point for x & y.

2. Solve for b3. Write your equation with your m and b.

Example 2: Write the equation of a line that has a

slope of -2 and goes through the point

(-2, -1).

1. Plug in m, x & y -1=-2(-2)+b2. Solve for b. -1 = 4 + b, b

= -53. Write equation with m & b

y = -2x - 5

Writing the equation: given the slope of a parallel line and a

point Using the slope-intercept form of a line

y= mx + b1. Remember that the slope of two

parallel lines are the same so just use the slope of the line you are given.

2. Plug in m, x & y.3. Solve for b.4. Write your equation with your m

and b.

Example 3 Write an equation of a line that goes through

the point (-5, 5) and is parallel to the line y = -8/5 x + 5.

1. Since the new line is parallel to the one given they have the same slope, m = -8/5.

2. Plug in m, x & y. 5 = -8/5(-5) + b3. Solve for b. b = -34. Write your equation with your m and b.

y = -8/5 x - 3

Writing an equation:Given a point and perpendicular line

Using the slope-intercept form of a line

y= mx + b

1.Remember that the slope of two perpendicular lines are negative reciprocals, so find the negative reciprocal of the slope of the line given and use that as m.

2. Plug in m, x & y.3.Solve for b.4. Write your equation with your m and b.

Example 4 Find an equation of a line that goes

through the point (-4,2) and is perpendicular to y = 2x +4

1. The slope of this line is 2, the negative reciprocal would be -1/2. So that will be the slope you use in your equation.

2. Plug in m, x & y. 2= -1/2(-4) +b 0 = b

3. Solve for b. 4. Write your equation with your m and b. y = -1/2 x + 0

Writing an equation:Given two points

Using the slope-intercept form of a line

y= mx + b 1. Find the slope between the two

points. 2. Plug in the slope and either one of

the points. 3. Solve for b. 4. Write your equation with m and b.

Example 5 Write an equation of a line that goes

through the points (0, -1) and (-3, 4).

1. Use the formula to find the slope of the line. m=-5/3

2. Plug in m, x & y. -1=-5/3(0) + b

3. Solve for b. -1 = b Write your equation with your m and

b. y = -5/3x -1

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