Download Equations of Lines - Intermediate Algebra - Assignment and more Exercises Algebra in PDF only on Docsity!
Intermediate Algebra Name _____________________________
Finding Equations of Lines
Finding equations from graphs: steps:
- Find the y -intercept. (0, b)
- Find the slope.
- Plug into slope-intercept formula y mx b.
- Put into function notation by replacing y with f ( x ). f ( x ) mx b
Ex 1: Slope: down 1, right 1 m = - 1 y - int: (0, 5), so b= Therefore, y x 5 f ( x ) x 5
Ex 2 : Slope: up 1, right 2 m = ½ y - int: (0, 2), so b= Therefore, 2 2
1 y x
2 2
1 f ( x ) x
You try: Find the equations of each line.
_________________ _________________ _________________ __________________
Finding Equations given a point and a slope: steps:
- Plug the point ( x 1 , y 1 )and the slope, m , that was given into the point-slope formula y y 1 m ( x x 1 ).
- Solve for y to get into slope intercept form: y mx b.
- Put into function notation by replacing y with f ( x ). f ( x ) mx b
Ex: Write an equation for a line with slope,
m , and goes through the point (8, -2).
x
y
x
y
x
y
x
y
run
rise m
- Write an equation for the line with slope, 5
m^ ,
and it goes through the point (-10, -2).
- Write an equation for the line with slope,
m , and goes through the point (-8, 0).
- Write an equation for the line with slope, m 0 , and goes through the point (5, -4). 4. Write an equation for the line with slope, m undefined , and goes through the point (2, 7).
Finding Equations given 2 points: steps:
- Calculate the slope. 2 1
2 1 x x
y y m
- Use the slope, m , and choose either point to plug into the point-slope formula y y 1 m ( x x 1 ).
- Solve for y to get into slope intercept form: y mx b.
- Put into function notation by replacing y with f ( x ). f ( x ) mx b
Ex: Write an equation for a line that goes through the points (4, -3) and (-6, 2).
- Write an equation for the line that goes through the point (6, -1) and parallel to the graph of 2 x 3 y 12. 2. Write an equation for the line that goes through the point (-2, 2) and perpendicular to the graph of 4 x 2 y 6.
- Write an equation for the line that goes through the point (-4, 5) and perpendicular to the graph of 3 y 15. 4. Write an equation for the line that goes through the point (3, -7) and parallel to the graph of x 2.
- Write an equation for the line that goes through the point (2, 3) and parallel to the line that goes through the points (2, 8) and (4, 0). 6. Write an equation for the line that goes through the point (6, 9) and perpendicular to the line that goes through the points (0, -2) and (-5, 8).
