Answer:
Line 1 and Line 2: Perpendicular
Line 1 and Line 3: Neither
Line 2 and Line 3: Neither
Step-by-step explanation:
In order to find the relationship between the pair of lines, we need to find the slope of each line.
Slope is same for parallel lines.
For perpendicular lines, slope of one line is equal to the negative reciprocal of the slope of the other line.
Standard form of an equation of line is [tex]y=mx+b[/tex].
Where, [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.
Convert lines 1, 2 and 3 in standard form.
Line 1:
[tex]10x+6y=8\\6y=-10x+8\\y=\frac{-10x+8}{6}\\y=-\frac{5}{3}x+\frac{4}{3}[/tex]
Slope, [tex]m_{1}=-\frac{5}{3}[/tex]
Line 2:
[tex]y=\frac{3}{5}x-7[/tex]
Slope, [tex]m_{2}=\frac{3}{5}[/tex]
Line 3:
[tex]3y=5x+2\\y=\frac{5}{3}x+\frac{2}{3}[/tex]
Slope, [tex]m_{3}=\frac{5}{3}[/tex]
From the above, we conclude that:
[tex]m_{1}=-\frac{1}{m_{2}}\\[tex]
The above condition is true for perpendicular lines.
Therefore, line 1 and line 2 are perpendicular to each other.
Slopes of line 2 and line or line 1 and line 3 don't have the relation for parallel lines or perpendicular lines. So, no relationship between them.
