Write an equation in slope intercept form for the line that is parallel to y = x - 6 and that passes through the point (-5, -6)

y = x - 1

Step-by-step explanation:

First, determine your slope from the given equation y = x - 6

In slope intercept form: y = mx + b, the value for m is the slope.

By looking at "x", there is a coefficient of 1 and therefore 1 is the slope.

Since parallel lines have the same slope, use the slope 1 to rewrite a second eqaution using

the point-slope formula: y - y1 = m(x - x1) and the given point (-5, -6)

y - y1 = m(x - x1)

y - (-6) = 1 (x - (-5))        (Plug in values)

y + 6   = 1(x + 5)            (Distribute negatives)

y + 6   = 1x  + 5             (Distribute 1 to both terms in the parentheses)

 - 6             - 6              (Subtract 6 from both sides)

   y = 1x - 1 OR y = x - 1  

Check your work by plugging in the given point to your equation:

y = x - 1

-6 = -5 - 1                   (Plug in values)

-6 = -6

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.