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3 years ago

Graph the line using a point and a slope. Write the equation of each line.

Mathematics

2 answers:

arsen [322]3 years ago

7 0

Answer:

y = -1/2x -3

Step-by-step explanation:

The line perpendicular to one with a slope of 2 will have a slope that is the negative reciprocal of 2, that is, -1/2. The given point is the y-intercept of the required line, so we can write its equation directly in slope-intercept form:

y = mx + b

where m is the slope (-1/2), and b is the y-intercept (-3). Your line is ...

y = -1/2x -3

8090 [49]3 years ago

7 0

Answer:

$y=-\frac{x}{2}-3$

Step-by-step explanation:

If two lines having slopes $m_1$ and $m_2$ are perpendicular,

$m_1\times m_2=-1$

Thus, if the slope of the line perpendicular line with slope 2 is m,

Then,

$m\times 2=-1\implies m = -\frac{1}{2}$

Now, the equation of the line passes through $(x_1, y_1)$ with slope m is,

$y-y_1=m(x-x_1)$

Hence, the equation of the line contain (0, -3) with slope $-\frac{1}{2}$ is,

$y+3=-\frac{1}{2}(x-0)$

$y=-\frac{1}{2}x-3$

Graphing :

if x = 0, y = -3,

if y = 0, $-\frac{x}{2}=3$ ⇒ x = -6

Thus, by joining the points (0, -3) and (-6, 0) we will get the graph of the given line.

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Factor 3/4 out of 3/4z + 6

Alenkasestr [34]

ANSWER

$\frac{3}{4} z + 6 = \frac{3}{4} (z + 8 )$

EXPLANATION

We want to factor
$\frac{3}{4}$
out of

$\frac{3}{4} z + 6$

The first term is already having a factor of
$\frac{3}{4}$
The constant term which is the second term is not having a factor of
$\frac{3}{4}$
so we need to use a trick of multiplying and dividing by the same factor to obtain,

$\frac{3}{4} z + 6 = \frac{3}{4} z + \frac{3}{4} \times \frac{6}{ \frac{3}{4} }$

We can now factor
$\frac{3}{4}$
out of the right hand side to obtain,

$\frac{3}{4} z + 6 = \frac{3}{4} (z + \frac{6}{ \frac{3}{4} } )$
Let us rewrite the right most fraction using the normal division symbol.

$\frac{3}{4} z + 6 = \frac{3}{4} (z + 6 \div \frac{3}{4} )$

We simplify to obtain,

$\frac{3}{4} z + 6 = \frac{3}{4} (z + 6 \times \frac{4}{3} )$

This further gives us,

$\frac{3}{4} z + 6 = \frac{3}{4} (z + 2 \times 4 )$

$\frac{3}{4} z + 6 = \frac{3}{4} (z + 8 )$

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3 years ago

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xenn [34]

0.05 then divide each number by 50% then simplify or if it’s a small number then just leave it

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3 years ago

Find the sum of the first six terms of a geometric series in which a1 = 4 and r = -3: A. 729 B. -729 C. -728 D. 728 plz help

natta225 [31]

Answer:

Step-by-step explanation:

The sum to n terms of a geometric sequence is

$S_{n}$ = $\frac{a_{1}(r^n-1) }{r-1}$

Here a₁ = 4 and r = - 3, thus

$S_{6}$ = $\frac{4((-3)^6-1)}{-3-1}$

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2 years ago

Which ordered pair would form a proportional relationship with the point graphed below? On a coordinate plane, a line with negat

avanturin [10]

Answer:

Answer:

(5, 20)

Step-by-step explanation:

We can find the slope of the line

m = (y2-y1)/(x2-x1)

= (40-0)/(10-0)

= 40/10

Since the line goes through (0,0) the y intercept is 0

y = mx+b

y = 4x

Lets check the points by substituting into the equation

40, 10) 10 = 4*40 10 =160 no

(–5, –10) -10 = 4*-5 10 = -20 no

(5, 20) 20 = 4*5 20 = 20 yes

(–10, –20) -20 = 4*-10 -20 = -40 no

Step-by-step explanation:

Which ordered pair would form a proportional relationship with the point graphed below? On a coordinate plane, a line with negative slope goes through points (negative 20, 10), (0, 0), and (20, negative 10). (10, –20) (–30, 20) (–10, 5) (35, –20)

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Nitella [24]

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