Question

Rewrite each equation in slope-intercept form, if necessary. Then determine
whether the lines are perpendicular. Explain.
36. Y = -x-7
37. Y=3
38. 2x - 7y= -42
y-x=20
x= -2
4y = -7x-2​

Answer 1

Slope intercept form as a general equation can be represented as:

y=mx+c

Representation: here m is represents the slope of the line while c represents the constant.

for the first equation

y=-x-7

we can rewrite the equation as:

y=-1X x -7

Comparing it to the general slope- intercept find we find that

m=-1 while c=-7

equation 2.

y=3

y=0Xx+3

so, m=0 and c=3

equation 3.

2x-7y=-42

2x=7y-42

2x+42=7y

y=$\frac{2}{7}$ X x+$\frac{42}{7}$

y=2/7 X x+6

So, m=2/7 while c=6;

equation 4.

y-x=20

y=20+x

y=1 X x+ 20

So, m=1 while c=2

From the property that states the slope of two perpendicular lines is -1.

So m1 x m2=-1

so, m1 = -1/m2

we can see that the slope of the first equation and the slope of the fourth equation have a product of -1.

1 X-1=-1

Thus the first and the fourth line are perpendicular to each other.

equation 5.

x=-2

0 X y + x=-2

0 X y = -x - 2

m=-1 and c=-2

equation 6.

4y=-7x-2

y=-7/4x-2/4

m=-7/2 while c=4/2; c=1/2

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