15. tell whether the lines for each pair of equations are parallel perpendicular or neither
y=-3x+7
-2x+6y=3
16. tell whether the lines for each pair of equations are parallel perpendicular or neither
y=-1/5x+6
-2x+10y= 5

Step-by-step explanation:

15. The given lines are

Y=-3x+7 & -2x+6y=3 or, 6y = 3 + 2x or, .

The slope of the first line is -3 and the slope of the second line is [Comparing with the standard form of equation of straight line y = mx + c, where m is the slope of the straight line].

Two straight lines will said to be perpendicular to each other, if the product of its slopes will be equal to -1.

Since, , the equations are perpendicular with respect to each other.

16. The lines are and -2x + 10y = 5 or, 10y = 5 + 2x or, .

As per the question number 15, it is clear that these equations are not perpendicular.

Here, the slope of the first one is and the slope of the second one is .

The values are same with different sign. Hence, these equations are not parallel too.

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)