Section 2-5: Writing Equations of Lines

Goal: Write a linear equation.

Warm-Up Exercises 1. Given the equation of the line 2x – 5y = 15,

solve the equation for y and identify the slope of the line.

2. What should the slope of a second line be if that line must be perpendicular to the first line?

Writing an Equation of a line Slope-Intercept

Form

◦ Given the slope m and the y-intercept b, use slope-intercept form: y=mx+b

Point Slope Form

◦ Given the slope m and a point (x1, y1), use point-slope form:

y - y1 = m(x - x1 )

Example 1: Write an equation given slope and y-intercept

Checkpoint: Write an equation of the line that has the given

slope and y-intercept.1. m = 3 b = 1 2. m = -2 b = -4 3. m = ½ b = -5

Example 2: Write an equation given slope and a point Write an equation of the line that passes

through (4,2) and has a slope of -¼ .

Example 2: additional exercises Write an equation of the line that passes

through (9, 2) and has a slope of – 1/3 .

Write an equation of the line that passes through the given point and has the given slope. Write your equation in slope-intercept form.

1. (-1, 3) m = 2 2. (4, -5) m = -3 3. (-2, 4) m = 5

Checkpoint:

Write an equation of the line that passes through (-1, 4) and is parallel to the line y = -2x + 5

Example 3: Write Equations of Parallel Lines

Write the equation of the line that passes through (2, 1) and is parallel to the line y = 3x + 10.

Example 3: Additional Exercises

Write an equation of the line that passes through (-1, 4) and is perpendicular to the line y = -2x + 5.

Example 4: Write equations of perpendicular lines

Write an equation of the line that passes through (2, 1) and is perpendicular to the line y = 3x + 10.

Example 4: additional exercises

Checkpoint: Write an equation of the line described.

1. Passes through (-6, -5); parallel to y = -x + 2

2. Passes through (-6, -5); perpendicular to y = -x + 2

Homework: