Problems in math

Question

1)Find the slope of the line 4x-3y-7=0

2)Find the equation of a line that passes through (-1,6) and (2,3)

3) Simplify the rational expression 3x²-7x

                                                                 ^{---------- =3}

                                                                      ²

Answer 1

For #3:

 

Simplify the rational expression (3x²-7x)/2=3

 

3x²-7x=6; multiply both sides by 2

 

3x²-7x-6=0, solve for x

 

(3x+2)(x-3)=0

 

x=-(2/3) or x=3.

 

Answer 2

1. transform into slope-intercept. A. add 7.(NOW:4x - 3y =7) B. subtract 4x (NOW: -3y = -4x + 7) C divide by -3 (NOW: 4/3x + 7/4). Slope is 4/3

 

2. do rise over run. A. y2 -y1/x2 -x1. (NOW: 3 - 6/2 - - 1: -3/3.. simplify to -1). Slope is -1.  B.Now plug into either value-pair in slope-intercept to find "b". y= -1x +b....6 = -1(-1) + b. b = 5. Equation is y = -1x + 5 or x +y = 5

 

3 No time for 3d . but hint: complete the square to solve.

Answer 3

1)

 

Solve for y from the equation.

 

Add 3y to both sides of the equation.

 

4x - 7 = 3y

 

 

Divide both sides of the equation by 3.

 

(4/3)x - (7/3) = y

 

 

The slope of the line is the coefficient of x.

 

 

2)

 

We can use the point-slope form of the line.

 

y - y₁ = mx - mx₁

 

 

-mx + y = -mx₁ + y₁     ------> standard form

 

y = mx - mx₁ + y₁   -------->  slope-intercept form

 

 

All you have to do is find the slope between the two points and plug in the coordinate values of any of the given points (x₁ , y₁).

 

 

3)

 

Factor out an x in the numerator.

 

x(3x - 7) / 2 = 3

 

 

There isn't much you can do from this point, other than solve for x.