Answer:
(a) Same slope and different y intercept
Step-by-step explanation:
Given
[tex]y = \frac{3}{7}x + 11[/tex]
[tex]-3x + 7y = 13[/tex]
Required
Are the lines, parallel?
To do this, we first convert both equations to slope intercept;
[tex]y = mx+ b[/tex]
Where
[tex]m = slope[/tex]
So, we have:
[tex]y = \frac{3}{7}x + 11[/tex]
[tex]-3x + 7y = 13[/tex]
Solve for 7y
[tex]7y = 3x + 13[/tex]
Solve for y
[tex]\frac{7y}{7} = \frac{3x}{7} + \frac{13}{7}[/tex]
[tex]y = \frac{3}{7}x + \frac{13}{7}[/tex]
So, the two equations are now:
[tex]y = \frac{3}{7}x + 11[/tex]
[tex]y = \frac{3}{7}x + \frac{13}{7}[/tex]
When two lines have the same slope but different y intercepts, then they are parallel.
Recall that:
In [tex]y = mx + b[/tex]
[tex]m = slope[/tex]
[tex]b = y \ intercept[/tex]
So:
In [tex]y = \frac{3}{7}x + 11[/tex] and [tex]y = \frac{3}{7}x + \frac{13}{7}[/tex]
The slopes are:
[tex]m = \frac{3}{7}[/tex] and [tex]m = \frac{3}{7}[/tex]
The y intercepts are:
[tex]b = 11[/tex] and [tex]b = \frac{13}{7}[/tex]
Since the values of m (the slope) are the same and the values of b (the y intercepts) are differenr, then they are parallel
