Find the slope, y-intercept, and the equation.

9514 1404 393

Step-by-step explanation:

The two-point form of the equation of a line can be used.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

For the two points, we choose to use ones near (0, 0):

  (x1, y1) = (-8, -14)  and  (x2, y2) = (14, 52)

Then our equation is ...

  y = (52 -(-14))/(14 -(-8))(x -(-8)) -14

  y = 66/22(x +8) -14

  y = 3x +24 -14

  y = 3x +10 . . . . . the equation

The slope is the coefficient of x: 3.

The y-intercept is the added constant: 10, or coordinates (0, 10).

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°