to find slope : difference of y / difference of x

slope-intercept form: y = m x + b where m = slope ; b = yintercept

2. parallel means, same slope.

3. solve for x: x2(squared) – 4x = 12

x^2 – 4x – 12 = 0

( x – 6) ( x + 2 )

x = 6 , -2

4. solve ofr x: 5/x+2 = 2

5 / (x+2 ) = 2 — multiply by x+2

5 = 2x + 4 — subtract 4

1 = 2x — divide by 2

x = 1/2

5. factor: 2×2(squared) – x – 15

( x – 3 )( 2x + 5)

6. factor: 3×2(squared) + 6x – 9

( 3x – 3 ) ( x + 3 )

1. Triangle ABC we need to find a line that intersects point B (-2,2) and the midpoint of line AC. So first lets find the midpoint of AC:

midpoint formula = (x1+x2)/2 , (y1+y2)/2

X = (1-0)/2 = 1/2

Y = (3+5)/2 = 4

So the midpoint is (1/2, 4)

Now, to calculate the slope (m) of a line that passes through two points we use this formula:

m = (y2 – y1)/(x2-x1)

(4 – 2)/(1/2 – -2)

m= 2/(2.5) = .8 = 4/5 (fractions are easier to work with)

Now finally lets find out the equation of a line with slope 4/5 that passes through our points.. either B or D work.

Equation: y – y1 = m(x-x1)

y-2 = 4/5(x-(-2))

y = 4/5x + 8/5 + 2

y= 4/5x +18/5

y= 4/5x + 3.6

The median BD of Triangle ABC is defined by y = 4/5x + 3.6

For #2, are you sure the line is parallel to BC and NOT BD? If it’s parallel to line BC it does not require information from #1 to solve.

I am going to assume that the line needs to be parallel to BD, and that you had a typo in your question:

We have the slope of line BD: m=4/5 So now we just need to repeat the last step and find a line with slope 4/5 that passes through point A (1,3). And it needs to be in point-slope form.

point-slope formula is y-y1 = m(x-x1) so it’s just fill in the blank:

Point A = (1, 3)

Slope (m) = 4/5

y – 3 = 4/5 (x-1)

Line AE in point-slope form is defined by the equation y-3 = 4/5 (x-1).

If your original post was not a typo, then it does not require information from question 1, and we just need to calculate the slope of line BC and substitute it for m.

3, 4, 5, and 6 are solved on other posts.

3. x^2 – 4x = 12

x^2 – 4x – 12 = 0

(x-6) (x+2) = 0

x = 6 and x = -2

4. 5/ x+2 = 2

5 = 2 (x+2)

= 2x + 4

2x = 5 – 4 = 1

x = 1/2

5. 2x^2 -x -15 = 0

(2x +5) (x-3) = 0

x = -2 1/2 and x = 3

6. 3x^2 + 6x – 9 = 0

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

x = 1 and x = -3

3.

x^2 – 4x – 12 = 0

x^2 – 6x + 2x – 12 =0

x(x- 6) + 2(x – 6) = 0

(x+2) (x-6) = 0

x = -2 , 6

4.

5/(x+2) = 2

5 = 2x + 4

2x = 1

x = 1/2

5.

2x^2 – x – 15 = 0

2x^2 – 6x + 5x – 15 = 0

2x(x – 3) + 5(x – 3) = 0

(2x + 5) (x – 3) = 0

x = -5/2 , 3

6.

3x^2 + 6x – 9 = 0

3x^2 + 9x – 3x – 9 =0

3x(x + 3) – 3(x + 3) = 0

(3x – 3) (x + 3) = 0

x = 1 , -3