MATH 140 -- Intermediate Algebra -- Exercise Solutions
Section: 3.4

2. Find the slope of the line through the points (1, 6) and (7, 11).
Solution: Let P₁ = (7, 11) and P₂ = (1, 6)

                  

4. Find the slope of the line through the points (2, 9) and (6, 4).
Solution: Let P₁ = (2, 9) and P₂ = (6, 4)

                  

6. Find the slope of the line through the points (3, 7) and (-2, 11).
Solution: Let P₁ = (3, 7) and P₂ = (-2, 11)

                  

8. Find the slope of the line through the points (- 3, - 4) and (- 1, 6).
Solution: Let P₁ = (- 3, - 4) and P₂ = (- 1, 6)

                   

10. Find the slope of the line through the points (3, - 1) and (- 6, 5).
Solution:
                 

12. Find the slope of the line through the points (4, 2) and (4, 0).
Solution:
                   

14. Find the slope of the line through the points (- 2, - 5) and (3, - 5).
Solution:
                  

26. Find the slope and y-intercept of the linear function whose rule is f(x) = - 2x + 6
Solution: Compare this rule with the rule f(x) = mx + b in the definition of a linear function where m (the coefficient of x) is the slope and b (the constant term) is the y-intercept.
From that comparison we see that the slope of f(x) = - 2x + 6 is - 2 and its y-intercept is 6.

28. Find the slope and y-intercept of the linear function given by the equation - 5x + y = 10.
Solution: Write the equation in slope_intercept form by solving for y to obtain y = 5x + 10.
Compare that equation with y = mx + b where m (coefficient of x) is the slope and b (constant term) is the y-intercept.
From that comparison we see that the slope of - 5x + y = 10 is 5 and its y-intercept is 10.

30. Find the slope and y-intercept of the linear function given by the equation - 3x - 4y = 6.
Solution: Write the equation in slope_intercept form by solving for y to obtain .
Compare that equation with y = mx + b where m (the coefficient of x) is the slope and b (the constant term) is the y-intercept.
From that comparison we see that the slope of - 3x - 4y = 6 is  and its y-intercept is  .

32. Find the slope and y-intercept of the linear function whose rule is
Solution: Compare this rule with the rule f(x) = mx + b in the definition of a linear function where m (the coefficient of x) is the slope and b (the constant term) is the y-intercept.
From that comparison we see that the slope of is and its y-intercept is 0.