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2 years ago

HELP HELP HELP Just 5 quick algebra 1 questions for 50 points!

Mathematics

1 answer:

riadik2000 [5.3K]2 years ago

4 0

1. x = a

2. y = b

3. It has an undefined slope.

4. You can either use, rise/run or change in y / change in x.

5. Rewrite the given equation in slope-intercept form, then determine the y-intercept, b, of the line.

<h3>What is the Equation of a Line?</h3>

Equation of a line with m as slope and b as y-intercept is given as: y = mx + b.

1. Vertical lines have undefined slope. This implies that, for a given point, (a, b), the equation that models the line would be expressed as x = a, where a is the x-intercept.

Vertical line equation is: x = a.

2. Horizontal lines have 0 as a slope value, therefore, given (a, b), the equation that models the line is: y = b.

3. Equation for a vertical line cannot be written in slope-intercept form because the slope for a vertical line is undefined.

4. Using the following, rise/run or change in y / change in x, the slope (m), can be calculated given the coordinates of two points on a line.

5. To find an equation in point-slope form, e.g. y - 3 = 6(x - 4), rewrite the equation in slope-intercept form:

y - 3 = 6x - 24

y = 6x - 24 + 3

y = 6x - 21

The y-intercept, b, is: -21.

Therefore, the coordinate of the y-intercept would be: (0, -21).

Learn more about the equation of a line on:

brainly.com/question/13763238

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Answer:

-3 is the value of the location where the line crosses the y-axis,and is commonly referred in the slope-intercept form of a line "the intercept". Now it may be your teacher expects you to answer this as the point on the plane where the y-intercept occurs, and that should be the point (0, -3). Make sure you follow your teacher's notation.

Step-by-step explanation:

Re-write the equation given in slope=intercept form by isolating the variable "y" on one side of the equation and expressing the rest in slope*x + y-intercet form:

$-2y-4x-6=0\\-4x-6=2y\\y=-2x-3\\$

which tells us that the slope of the line is -2 and it y-intercept is "-3".

Now, watch out because you may be asked to write the actual coordinates of the y-intercept, which are: (0, -3)

giving the x-coordinate 0 and the y-value where the line crosses the y-axis.

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8. If k = log, 3 then log, 48 =<br> 16<br> (1) 2k +3<br> (3) k +8<br> (2) 3k +1<br> (4) k +4

vekshin1

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Take the base-3/2 logarithm of both sides:

$\log_{3/2}\left(\dfrac32\right)^x = \log_{3/2}(3) \\\\ \implies x \log_{3/2}\left(\dfrac 32\right) = \log_{3/2}(3) \\\\ \implies \boxed{x = \log_{3/2}(3)}$

Alternatively, you can divide both sides by $3^x$ :

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Then take the base-2/3 logarith of both sides to get

$\log_{2/3}\left(2/3\right)^x = \log_{2/3}\left(\dfrac13\right) \\\\ \implies x \log_{2/3}\left(\dfrac23\right) = \log_{2/3}\left(\dfrac13\right) \\\\ \implies x = \log_{2/3}\left(\dfrac13\right) \\\\ \implies x = \log_{2/3}\left(3^{-1}\right) \\\\ \implies \boxed{x = -\log_{2/3}(3)}$

(Both answers are equivalent)

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