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9.
Write an equation for the line that is parallel to the given line and that passes through the given point.

y = 2^x + 7; (3, 11)

A. y = 2^x + 5

B. y = 1/2x + 5

C. y = -1/2x – 5

D. y = 2^x - 19

Sagot :

maddymcg408

Answer:

A. y = 2^x + 5

Step-by-step explanation:

The equation is not linear, so a constant slope does not exist.

Not Linear                     PARALLEL

...................................................................................................................................................

The equation is not linear, so a constant slope does not exist.

Not Linear                         PERPENDICULAR

...............................................................................................................................................

First, remember that if two lines are parallel, they have the same slope. The problem already gave us a point on the line and we now have the power to find the slope. Since we have the slope and a point on the line, we are going to find the equation of the line through the point-slope formula, which is:

 is a point on the line

is the slope of the line

The equation given to us has a slope of 2, as we can see because the line is in slope-intercept form. Also, we are given the point (3, 11), which we are told is on the line. Since we are already given all of the information for the point-slope formula, we can simply substitute it in and solve for the equation.

Set up

Use the Distributive Property on both sides

Add 11 to both sides and simplify

The equation of our line is y = 2x + 5.

...............................................................................................................................................

Slope-intercept form:

y = mx + b   "m" is the slope, "b" is the y-intercept (the y value when x = 0)

For lines to be parallel, they have to have the SAME slope.

The given line's slope is 2, so the parallel line's slope is also 2.

y = 2x + b

To find "b", plug in the point (3,11) into the equation.

y = 2x + b

11 = 2(3) + b      Multiply 2 and 3

11 = 6 + b      Subtract 6 on both sides

5 = b

y = 2x + 5

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