What is the equation of the line that is perpendicular to the line y=3/4x - 6 and passes through the point (-3,5)?

Step-by-step explanation:

Hi there!

What we need to know:

Linear equations are typically organized in slope-intercept form: where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)Perpendicular lines always have slopes that are negative reciprocals of each other (ex. -1/3 and 3, 1/2 and -2, etc.)

1) Determine the slope (m)

Looking at the given equation, we can identify clearly that is in the place of m, making it the slope of the line. Because perpendicular lines always have slopes that are negative reciprocals, we know that the slope of the line we're solving for will be . Plug this into :

2) Determine the y-intercept (b)

Plug in the given point (-3,5)

Subtract 4 from both sides

Therefore, the y-intercept is 1. Plug this back into :

I hope this helps!

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