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WARRIOR [948]
3 years ago
7

What is the y-intercept of a line perpendicular to y= 1/2x + 6 that passes through the point (4,-3)

Mathematics
1 answer:
zalisa [80]3 years ago
5 0

Answer:

(0,5)

Step-by-step explanation:

Perpendicular lines have slopes which are negative reciprocals of each other. The slope of the line y=1/2x + 6 is 1/2. The slope perpendicular to it is -2.

Using m=-2, substitute it and (4,-3) into the point slope form and simplify to find the y-intercept.

y-y_1 = m(x-x_1)\\y--3=-2(x-4)\\y+3=-2(x-4)\\y+3=-2x+8\\y=-2x+5

The equation is now in slope intercept form y=mx+b and b is the y-intercept. The y-intercept of y=-2x+5 is (0,5).

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9514 1404 393

Answer:

  (a)  x = (3 -ln(3))/5 ≈ 0.819722457734

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Step-by-step explanation:

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(b) Assuming "lg" means "log", the logarithm to base 10, we have ...

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The solution is ...

  y = 10

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When solving equations using a graphing calculator, it often works well to define a function f(x) such that the solution is f(x) = 0, the x-intercept(s). That form is easily obtained by subtracting the right side of the equation from both sides of the equation. In part (a) here, that is ...

  f(x) = e^(2x+1) -3e^(4-3x)

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