Hi Grace;

I believe I had the same instructor. In college, he would talk endlessly. He once had his hands in his jacket pockets when he began waiving his hands around without realizing that he forgot his hands were still in his pockets. It was quite a spectacle.

**1. Decide whether the pair of lines is parallel, perpendicular, or neither.**

**3x-8y=-7 and 32x+12y=-7**

Both equations are in standard form...

Ax+By=C, neither A nor B equal zero, and A is greater than zero.

Slope is -A/B...

-[(3)/(-8)]

A negative of a negative is positive...

3/8

Slope is -A/B...

-[(32)/(12)]

Both numbers are divisible by 4...

-8/3

One slope is the negative inverse of the other.

**THESE ARE PERPENDICULAR LINES.**

**2. Find the slope-intercept form of the line satisfying the conditions.**

**m=7/4; through (0,3)**

Slope-intercept equation is...

y=mx+b

m is the slope.

b is the y-intercept, the value of y when x=0. This is the point provided.

**y=(7/4)x+3**

**3. Find an equation of the line satisfying the conditions. Write the equation in slope-intercept form.**

**Through (-3,8); perpendicular to -3x+4y=-23**

The equation is not in standard format because A is less than zero. Let's fix that by multiplying both sides by -1...

(-1)(-3x+4y)=-23(-1)

3x-4y=23

It does not make a difference when establishing slope. But I go by the rules because when you enter the higher levels of algebra, it will matter.

Slope is -A/B...

-[(3)/(-4)]

3/4

The slope of the line perpendicular to this is its negative inverse...

-4/3...

Slope-intercept form is...

y=mx+b

y=(-4/3)x+b

Let's plug-in the one point provided, (-3,8), to establish the y-intercept, b.

8=[(-4/3)(-3)]+b

Note how the 3 in the numerator and denominator cancels, -3/3=-1...

8=[(-4)(-1)]+b

A negative number multiplied by a negative number has a positive result...

8=4+b

Let's subtract 4 from both sides...

8-4=4-4+b

4=b

y=(-4/3)x+4

**4. Through (-6,7); parallel to 3x+7y=3**

The equation is in standard form. The slope is -A/B.

-[(3)/(7)]=-3/7

The slope of the line parallel to this is the same.

y=(-3/7)x+b

Let's plug-in the one point provided...

7=[(-3/7)(-6)]+b

7=(18/7)+b

Let's convert 7 into 49/7...

49/7=(18/7)+b

Let's subtract 18/7 from both sides...

(49/7)-(18/7)=-(18/7)+(18/7)+b

31/7=b

**y=(-3/7)x+(31/7)**

**5. Find an equation of the line passing through the two points. Write the equation in standard form.**

**(-7,-5) and (2,5)**

Let's first establish slope. Slope is change-of-y divided by change-of-x...

(y-y_{1})/(x-x_{1})

(-5-5)/(-7-2)

-10/-9

A negative number divided by a negative number has a positive result...

10/9

Standard formula is...

Ax+By=C, neither A nor B equal zero, and A is greater than zero...

Slope is -A/B.

Slope is -(10/9)

Because A must be greater than zero, this is...

10/-9

10x-9y=C

Let's plug-in one point provided to establish the value of C. I randomly select the first, (-7,-5)...

[(10)(-7)]-[(9)(-5)]=C

-70+45=C

-25=C

**10x-9y=-25**

Let's use the other point provided, (2,5), to verify the result...

[(10)(2)]-[(9)(5)]=-25

20-45=-25

-25=-25

## Comments

1chapter and everyone is still lost. Anyway, thanks for your response! :)