A line passes through the point (-10,-1) and is parallel to the line with equation y=2x-9

        y = 2x + 19

Step-by-step explanation:

y=m₁x+b₁   ║   y=m₂x+b₂   ⇔    m₁ = m₂

{Two lines are parallel if  their slopes are equal}

y = 2x - 9    ⇒   m₁ = 2    ⇒    m₂ = 2

The point-slope form of the equation of a line: y - y₁ = m(x - x₁),

m is the slope and (x₁, y₁) is the point the line passes through.

m = 2

(-10, -1)   ⇒   x₁ = -10,  y₁ = -1

point-slope form:

y - (-1) = 2(x - (-10))

y + 1 = 2x + 20            {subtact 1 from both sides}

y = 2x + 19        ←    slope-intercept form

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

Answers4.) -1/205.) -1/406.) -55/127.) -3/4