Question

The equation of line j is6x+5y=3,and the equation of line q is 5x–6y=0. Which statement about the two lines is true? Help

Answer 1

A. Lines j and q have the same y-intercept.
B. Lines j and q are parallel.
C. Lines j and q have the same x-intercept.
D. Lines j and q are perpendicular.

Answer 2

we will compare the slopes and the y intercepts.
In y = mx + b form, the slope is in the m position and the y intercept is in the b position.

6x + 5y = 3 -- subtract 6x from both sides
5y = -6x + 3 -- divide both sides by 5
y = -6/5x + 3/5
In this one, the slope is -6/5 and the y intercept is 3/5
x intercept can be found by subbing in 0 for y
6x + 5(0) = 3
6x = 3
x = 1/2...x intercept is 1/2

5x - 6y = 0 -- subtract 5x from both sides
-6y = -5x + 0 -- divide both sides by -6
y = 5/6x - 0
In this one, the slope is 5/6 and the y intercept is 0
x intercept..sub in 0 for y
5x - 6(0) = 0
5x = 0
x = 0...x intercept is 0

we can now see that they do not have the same x and y intercepts, so A and C are eliminated. Also, for the lines to be parallel, they have to have the same slope, which they do not, so that eliminates B. Thus, leaving us with D.

Perpendicular lines will have negative reciprocal slopes. All that means is " flip " the slope and change the sign.
Example :
1/2.....negative reciprocal is -2/1, or just -2...see how I flipped the slope and changed the sign. So 1/2 and -2 are negative reciprocals of each other and are therefore, perpendicular.

Now look at answer choice D.....one of the slopes is -6/5...." flip it " and change the sign...it then becomes 5/6.
-6/5 and 5/6 are negative reciprocals of each other and are perpendicular.
D is your answer.

Answer 3

Thank you

Answer 4

YW :)