5. Equations of Lines: slope intercept & point slope
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1 5. Equations of Lines: slope intercept & point slope Slope of the line m rise run Slope-Intercept Form m + b m is slope; b is -intercept Point-Slope Form m( + or m( Slope of parallel lines m m (slopes are the same Slope of perpendicular lines m m (slopes are opposite & reciprocal Equations of Horizontal and Vertical Lines b horizontal line a vertical line, where a & b are constants Eample (: Write the slope - intercept equation of a line which passes through (0,-7 whose slope is. -intercept ( 0,b, and the problem provides both information. m + b. What we need to complete this equation are slope ( m and b 7 The equation of the line is 7 0,4 and Eample (: Write the slope-intercept equation of a line which passes through ( (, 5. m + b. What we need to complete this equation are slope ( -intercept ( 0,b, however, we onl have -intercept To find the slope, m 0 m and b 4 The equation of the line is + 4 This instructional aid was prepared b the Learning Commons at Tallahassee Communit College.
2 Eample (: Write the slope-intercept equation of a line which passes through (,4 slope is 5. whose m + b. What we need to complete this equation are slope ( 0, however, we onl have slope. Here there are two was to find the equation of the line. -intercept (,b Method I We will substitute m 5, (,,4 ( in the form m + b to solve for b. m and (, 4 5( + b > b 9 The equation of the line is Method II Since we are given slope m and an ordered pair ( equation of the line.,, we can use Point-slope form to find m + Point-slope form is ( m 5, (, (,4 ( ( > 5 ( > > Simplif the parenthesis Distribute 5 into parenthesis ( 5, Eample (4: Write the slope-intercept equation of a line which passes through (,. -intercept (,b and m + b. What we need to complete this equation are slope ( 0. However, we are given two ordered pairs ( and ( without slope and -,, intercept. Therefore, we need to find the slope first. Then we can use the two methods discussed on Eample ( to find the equation of the line. This instructional aid was prepared b the Learning Commons at Tallahassee Communit College.
3 ( ( To find the slope between two ordered pairs, (, and ( 5, m Method I Now we have slope, we will substitute m and ( m, ( (,, ( + b in the form m + b to solve for b. > 7 b The equation of the line is + 7 Method II We also can use Point-slope form to find the equation of the line. m + Point-slope form is ( m, ( (,, ( + > + Distribute into parenthesis > > Combine like term Eample (5: Write the slope-intercept equation of a line which is parallel to 4 passing through (,., m + b. What we need to complete this equation are slope ( 0. Since the line we re looking for is parallel to 4, their slopes are the same, -intercept (,b m 4. Method I We will substitute m and (, m 4, ( (, 4( + b, in the form m + b to solve for b. > b The equation of the line is 4 This instructional aid was prepared b the Learning Commons at Tallahassee Communit College.
4 Method II We also can use Point-slope form to find the equation of the line. m + Point-slope form is ( (, m 4, (, ( 4 + > > 4 Distribute 4 into parenthesis Combine like term Eample (6: Write the slope-intercept equation of a line which is perpendicular to + 4, passing through (,5 -intercept (,b. m + b. What we need to complete this equation are the slope ( 0. Since our line is perpendicular to + 4 (which was given, we can find the slope of our line b taking the opposite sign and using the reciprocal of the given line which has a slope of m. Therefore, the slope of our line is m (the perpendicular one to the given line Method I We will substitute m and (, m + m, ( (,5 5 ( + b, in the form b to solve for b. > b > b 4 The equation of the line is + 4 Method II We also can use Point-slope form to find the equation of the line. m + Point-slope form is ( m, (, (,5 ( ( 5 + > ( > > + 4 Simplif the parenthesis Distribute 5 into parenthesis This instructional aid was prepared b the Learning Commons at Tallahassee Communit College. 4
5 Eample (7: Write an equation of a vertical line which passes through,6. The equation of a vertical line is a The -coordinate of the point,6 is. Therefore, the equation of the vertical line is Eample (8: Write an equation of a horizontal line which passes through 5, 4 6. The equation of a horizontal line is b The -coordinate of the point Eercises: 5, 4 6 is 5. Therefore, the equation of the horizontal line is Write the slope - intercept equation of a line which passes through (0,5 whose slope is 4., 4,5.. Write the slope-intercept equation of a line which passes through 0 and. Write the slope-intercept equation of a line which passes through 4,0 and 7,. 4. Write the slope-intercept equation of a line which is parallel to 5, passing through 6, 5. Write the slope-intercept equation of a line which is perpendicular to 7, passing through, 6. Write an equation of a horizontal line which passes through 5, 7. Write an equation of a vertical line which passes through 7 8,. Answers: This instructional aid was prepared b the Learning Commons at Tallahassee Communit College. 5
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