## Problems
__Problem 1:__
Find the equation of the line that passes through the points (-1 , 0) and (-4 , 12).
__Problem 2:__
What is the equation of the line through the points (-2 , 0) and (-2 , 4).
__Problem 3:__
Find the equation of the line that passes through the points (7 , 5) and (-9 , 5).
__Problem 4:__
Find the equation of the line through the point (3 , 4) and parallel to the x axis.
__Problem 5:__
What is the equation of the line through the point (-3 , 2) and has x intercept at x = -1.
__Problem 6:__
Find the equation of the line that has an x intercept at x = - 4 and y intercept at y = 5.
__Problem 7:__
What is the equation of the line through the point (-1 , 0) and perpendicular to the line y = 9.
__Problem 8:__
Find the slope, the x and y intercepts of the line given by the equation: -3 x + 5 y = 8.
__Problem 9:__
Find the slope intercept form for the line given by its equation: x / 4 - y / 5 = 3.
__Problem 10:__
Are the lines x = -3 and x = 0 parallel or perpendicular?
__Problem 11:__
For what values of b the point (2 , 2 b) is on the line with equation x - 4 y = 6
## Solutions to the Above Problems__Solution to Problem 1:__ The slope of the line is given by
m = (y2 - y1) / (x2 - x1) = (12 - 0) / (-4 - (-1)) = - 12 / 3 = - 4
We now write the equation of the line in point slope form: y - y1 = m (x - x1)
y - 0 = - 4(x - (-1))
Simplify and write the equation in general form
y + 4 x = - 4
__Solution to Problem 2:__
The two points have the same x coordinate and are on the same vertical line whose equation is
x = - 2
__Solution to Problem 3:__
The two points have the same y coordinate and are on the same horizontal line whose equation is
y = 5
__Solution to Problem 4:__
A line parallel to the axis has equation of the form y = constant. Since the line we are trying to find passes through (3 , 4), then the equation of the line is given by:
y = 4
__Solution to Problem 5:__
The x intercept is the point (-1 , 0). The slope of the line is given by:
m = (2 - 0) / (-3 - (-1)) = 2 / - 2 = -1
The point slope form of the line is
y - 0 = -1(x - (-1))
The equation can be written as
y = - x - 1
__Solution to Problem 6:__
The x and y intercepts are the points (-4 , 0) and (0 , 5). The slope of the line is given by:
m = (5 - 0) / (0 - (-4)) = 5 / 4
The point slope form of the line is
y - 5 = (5 / 4)(x - 0)
Multiply all terms by 4 and simplify
4 y - 20 = 5 x
__Solution to Problem 7:__
The line y = 9 is a horizontal line (parallel to the x axis). The line that is perpendicular to the line y = 9 have the form x = constant. Since the (-1 , 0) is a point on this line, the equation is given by
x = -1
__Solution to Problem 8:__
To find the slope of the given, we first write in slope intercept form
5y = 3x + 8
y = (3/5) x + 8 / 5
The slope is equal to 3/5. The y intercept is found by setting x = 0 in the equation and solve for y. Hence the y intercept is at y = 8/5. The x intercept is found by setting y = 0 and solve for x. Hence the x intercept is at x = -8/3
__Solution to Problem 9:__
Given the equation
x / 4 - y / 5 = 3
Keep only the term in y on the left side of the equation
- y / 5 = 3 - x / 4
Multiply all terms by -5
y = (5/4) x - 15
__Solution to Problem 10:__
The line x = - 3 is parallel to the y axis and the line x = 0 is the y axis. The two lines are parallel.
__Solution to Problem 11:__
For a point to be on a line, its coordinates must satisfy the equation of the line.
2 - 4(2 b) = 6
Solve for b
b = -1 / 2
## More References and LinksGeneral Equation of a Line: ax + by = c
Slope of a Line
Solve Slope Problems |