Which statement about the following equations is correct?

The equations are independent because the equations represent parallel lines.
The equations are independent because the lines intersect in one point.
The equations are dependent because the lines do not intersect.
The equations are dependent because the lines are the same line.

Question

Which statement about the following equations is correct?

The equations are independent because the equations represent parallel lines.
The equations are independent because the lines intersect in one point.
The equations are dependent because the lines do not intersect.
The equations are dependent because the lines are the same line.

UpStudy AI · Accepted Answer

1. The slope-intercept form of a line is given by $$ y = mx + b $$, where $$ m $$ is the slope.

2. For the first equation, $$ y = 2x + 5 $$, the slope is $$ m = 2 $$.

3. For the second equation, $$ y = -2x + 5 $$, the slope is $$ m = -2 $$.

4. Since $$ 2 
eq -2 $$, the lines have different slopes and are not parallel.

5. Two non-parallel lines will intersect at exactly one point, making the equations independent.

6. Therefore, the correct statement is:  
   **The equations are independent because the lines intersect in one point.**
The equations are independent because the lines intersect at one point.

Upstudy AI Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Algebra Questions