When we work with linear equations in two variables, it is sometimes useful to algebraically manipulate the equation into different forms. Here we will test our ability to move between slope-intercept form: y = mx + b, point-slope form: y - y_{1} = m (x - x_{1}), and standard form: ax + by = c.
Test Objectives:•Demonstrate the ability to write an equation in slope-intercept form
•Demonstrate the ability to write an equation in point-slope form
•Demonstrate the ability to write an equation in standard form
Forms of a Line Test:
#1:
Instructions: Write the slope-intercept form of the equation of each line.
a) m = -1, y-intercept: (0,-3)
b) m = 3, y-intercept: (0,5)
c) m = -4/3, y-intercept: (0,4)
#2:
Instructions: Write the slope-intercept form of the equation of each line.
a) m = -1, through (0,2)
b) m = -3/7, through (-3,5)
#3:
Instructions: Write the slope-intercept form of the equation of each line.
a) through (5,-4) and (0,1)
b) through (2,-1) and (-5,3)
#4:
Instructions: Write the standard form of the equation of each line.
a) m = -7/2, y-intercept: (0,-3)
b) m = 1/5, y-intercept: (0,-4)
#5:
Instructions: Write the standard form of the equation of each line.
a) through (-1,2) and parallel to: $$y = -2x - 2$$
b) through (-4,-1) and perpendicular to: $$y = -\frac{2}{3}x - 2$$
Written Solutions:
Solution:
a) $$y = -x - 3$$
b) $$y = -\frac{4}{3}x + 4$$
Solution:
a) $$y = -x + 2$$
b) $$y = -\frac{3}{7}x + \frac{26}{7}$$
Solution:
a) $$y = -x + 1$$
b) $$y = -\frac{4}{7}x + \frac{1}{7}$$
Solution:
a) $$7x + 2y = -6$$
b) $$x - 5y = 20$$
Solution:
a) $$2x + y = 0$$
b) $$3x - 2y = -10$$