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2 years ago

11

Write the equation of the line with a slope of - 2 and a y-intercept of (0, - 4) in slope-intercept form.

1 answer:

Olin [163]2 years ago

8 0

$\bf y=-2x\stackrel{\stackrel{(0,-4)}{\downarrow }}{-4}\impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}$

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Find an equation for the line that passes through the points (5.-5) and (-4,-2)

ANEK [815]

Answer:

$\large\boxed{y=-\dfrac{1}{3}x-\dfrac{10}{3}\to x+3y=-10}$

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

<em>m</em><em> - slope</em>

<em>b</em><em> - y-intercept</em>

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (5, -5) and (-4, -2).

Substiute:

$m=\dfrac{-2-(-5)}{-4-5}=\dfrac{-2+5}{-9}=\dfrac{3}{-9}=-\dfrac{1}{3}$

Put the value of the slope and the coordinates of the point (5, -5) to the equation of a line:

$-5=-\dfrac{1}{3}(5)+b$

$-5=-\dfrac{5}{3}+b$ <em>add 5/3 to both sides</em>

$-\dfrac{15}{3}+\dfrac{5}{3}=b\\\\-\dfrac{10}{3}=b\to b=-\dfrac{10}{3}$

Finally we have the equation of a line in the slope-intercept form:

$y=-\dfrac{1}{3}x-\dfrac{10}{3}$

Convert to the standard form <em>(Ax + By = C)</em>:

$y=-\dfrac{1}{3}x-\dfrac{10}{3}$ <em>multiply both sides by 3</em>

$3y=-x-10$ <em>add x to both sides</em>

$x+3y=-10$

4 0

3 years ago

Solve the system of equations.

Sloan [31]

Answer:

b.

( -3, -5)

Step-by-step explanation:

6x + 13 = 2x + 1

6x -2x = 1-13

4x = -12

x = -12/4 = -3

y = 6x + 13

y = 6(-3) +13 = -18+13 = -5

(x, y) = (-3,-5)

7 0

2 years ago

Read 2 more answers

Describe algebraically the relationship between x1 and x2

DanielleElmas [232]

X2 is double the amount of x1

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3 years ago

If the coordinates of A and B are (-3, a) and (1, a+4) respectively and the mid point of AB is (-1, 1),

goldfiish [28.3K]

$a=-1$

Using the midpoint formula directly from the topic meaning

$\frac{x_{1}+x_{2} }{2} or \frac{y_{1}+y_{2} }{2}$

so

$\frac{a+a+4}{2} =1\\a=-1$

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