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3 years ago

Describe all the x-values at a distance of 25 or less from the number 12. Enter your answer in interval notation.

Mathematics

1 answer:

Liula [17]3 years ago

6 0

Answer: [-13, 37]

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Explanation:

The smallest x value possible is 12-25 = -13

The largest x value possible is 12+25 = 37

It might help to draw out a number line to see this.

x is between -13 and 37, including both endpoints. We can write $-13 \le x \le 37$

This converts to the interval notation [-13, 37] which is the answer.

The use of square brackets is to indicate "include this endpoint".

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Use your understanding of transformations and key features to write the slope-intercept equation of this linear function.

sveta [45]

Answer:

$y = -2x + 5$

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Step-by-step explanation:

Hello!

Slope - Intercept Form: $y = mx+b$

m = slope
b = y-intercept

<h3>Slope</h3>

The slope of the line is the rate of change, or how the graph changes in y as it changes in x.

Slope can be calculated by the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$

We need two points on the line to get the x and y-values. I'm going to choose points (0,5) and (4,-3).

Calculate Slope

$m = \frac{y_2 - y_1}{x_2 - x_1}$
$m = \frac{5 - (-3)}{0 - 4}$
$m = -\frac{8}{4}$
$m = -2$

The slope is -2.

<h3>Y-intercept</h3>

The y-intercept of the line is where the graph touches the y-axis (x = 0). It can be found by looking at the intersection of the graph and the axis.

The intersection happens at point (0,5), so the y-intercept is 5.

<h3>Equation</h3>

We found m, the slope, to be -2 and b, the y-intercept, to be 5. We can just plug it into the equation format.

Equation: $y = -2x + 5$

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2 years ago

Passes through (2,2), slope = 3

nikdorinn [45]

Answer:

y - 2 = 3(x - 2)

Step-by-step explanation:

Hello!

Please consider using the point-slope formula for the equation of a straight line, because in this case it's the easiest way to go.

(2,2) is one point on the line, and the slope is m = -3.

Thus, y - k = m(x - h) becomes y - 2 = 3(x - 2).

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Step-by-step explanation:

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Describe all the x-values at a distance of 25 or less from the number 12. Enter your answer in interval notation.​

Describe all the x-values at a distance of 25 or less from the number 12. Enter your answer in interval notation.