Thread: Linear equations in two variables

Find the x and y intercepts and slope (if they exist) for the line given.
-2x + y = 14
x intercept Would it be (-2,0)
y intercept Would it be ( 0,4)
Slope Would it be 2

The slope of a line is 1/3
What is the slope of a line parallel to the given line? Would it be 1/3
What is the slope of a line perpendicular to the given line? Would it be -1/3

What if the slope (if it exists) of a line given by the equation x = -5? Would it be undefined?
Thanks

Originally Posted by rowdy3

Find the x and y intercepts and slope (if they exist) for the line given.
-2x + y = 14
x intercept Would it be (-2,0)
y intercept Would it be ( 0,4)
Slope Would it be 2

These points aren't even on the line! How can they be intercepts??

You got the slope right, though.

The x-intercept is where y = 0. Solve this for x.
The y-intercept is where x = 0. Solve this for y.

Originally Posted by rowdy3

The slope of a line is 1/3
What is the slope of a line parallel to the given line? Would it be 1/3
What is the slope of a line perpendicular to the given line? Would it be -1/3

Yes to the first, no to the second. Two perpendicular lines have slopes that have the following property:


So you know that .

Solve for .

Originally Posted by rowdy3

What if the slope (if it exists) of a line given by the equation x = -5? Would it be undefined?
Thanks

Yes. The slope of a line is rise/run. Consider two points on this line, say (-5, 1) and (-5, 6).

which is undefined.

-Dan

This is what I did.
y= 2x + 14
x- intercept 0= 2x + 14 14/2
x- intercept (7,0)
y- intercept y= 2(0) + 14
y- intercept (0,14)

The slope of a line is 1/3
1/3 * - 3/1 =-1
What is the slope of a line perpendicular to the given line? Is it -3/1

Originally Posted by rowdy3

This is what I did.
y= 2x + 14
x- intercept 0= 2x + 14 14/2
x- intercept (7,0)
y- intercept y= 2(0) + 14
y- intercept (0,14)

The slope of a line is 1/3
1/3 * - 3/1 =-1
What is the slope of a line perpendicular to the given line? Is it -3/1

This is correct except for your x-intercept. Again, isn't even on the line (since ). Your method is fine, but you made a slight mistake when solving for .

Write an equation of the line passing through the point (12, -10) having slope 4/3. Write your final answer in slope-intercept form.

Write an equation of the line passing through the point (0, 2) and parallel to the line x-y = 7. Write your final answer in slope-intercept form.

1. y+10= 4/3 ·(x- 12) My answer is y= 4/3·x -26

2. P(0,2) slope= 1--> y-2= 1(x-0) My answer is y= x + 2

Originally Posted by rowdy3

Write an equation of the line passing through the point (12, -10) having slope 4/3. Write your final answer in slope-intercept form.

Write an equation of the line passing through the point (0, 2) and parallel to the line x-y = 7. Write your final answer in slope-intercept form.

1. y+10= 4/3 ·(x- 12) My answer is y= 4/3·x -26

2. P(0,2) slope= 1--> y-2= 1(x-0) My answer is y= x + 2

Everything is OK

By the way: If you have a new question start a new thread. Otherwise you risk that no member of the forum will see that you need some additional help.