Write an equation of a line in slope-intercept form that passes through (-3,5) and is parallel to y = -6x +1. Then find its x- and y-intercepts.

a) The equation of the Parallel line to the given straight line is

       6 x + y + 13 =0

b) Slope - intercept form

        y = - 6 x - 13

c) The intercept - form

x - intercept  =  

y - intercept = - 13

Step-by-step explanation:

Step(i):-

Given the equation of the straight line

                             y = -6x +1

                  6 x + y - 1 = 0

The equation of the Parallel line to the given straight line is

                6x + y + k=0 and it passes through the point (-3, 5 )

           ⇒ 6 (-3 ) + 5 + k =0

          ⇒  - 18 + 5 + k=0

         ⇒   -13 + k = 0

        ⇒     k = 13

The equation of the Parallel line to the given straight line is

       6 x + y + 13 =0

Step(ii):-

Slope - intercept form

                y = m x + C

                y = - 6 x - 13

Step(iii):-

Intercept - form

              6 x + y + 13 =0

              6 x + y = - 13

The intercept - form

x - intercept  =  

y - intercept = - 13

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°