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3 years ago

Write an equation in slope-intercept for the line that goes

Mathematics

2 answers:

maksim [4K]3 years ago

8 0

Answer:

y = 1/3x - 4

Step-by-step explanation:

please mark me branliest tyyyy!! :))))))))))

svet-max [94.6K]3 years ago

7 0

Answer:

$y = \frac{1}{3} x-4$

Step-by-step explanation:

1) First, find the slope of the line. Use the slope formula, $m = \frac{y_2-y_1}{x_2-x_1}$ . Substitute the x and y values of the given points into the formula and solve:

$m=\frac{(-2)-(-3)}{(6)-(3)} \\m = \frac{-2+3}{6-3} \\m = \frac{1}{3}$

Thus, the slope is $\frac{1}{3}$ .

2) Next, write the equation of the line using the point-slope formula $y-y_1 = m (x-x_1)$ . (From there, we can convert it to slope-intercept form.) Substitute $m$ , $x_1$ , and $y_1$ for real values.

Since $m$ represents the slope, substitute $\frac{1}{3}$ for it. Since $x_1$ and $y_1$ represent the x and y values of one point the line intersects, substitute the x and y values of either one of the given points (it doesn't matter which one, it will equal the same thing) into the formula as well. I chose (3, -3), as shown below. From there, convert the point-slope form of the equation to slope-intercept form by isolating y:

$y-(-3) = \frac{1}{3} (x-3)\\y + 3=\frac{1}{3} x-1\\y = \frac{1}{3} x-4$

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Read 2 more answers

100 POINTS TO RIGHT AWNSER!!!!

makvit [3.9K]

If you're using the app, try seeing this answer through your browser: brainly.com/question/3000586

——————————

The answer is option D) r < 5 or r > – 1.

I'm going to graph each inequality below on a number line.

A) r > 5 or r > – 1.

$\large\begin{array}{cl} \mathsf{r>5}&\qquad\mathsf{\textsf{|||}\!\!\!\underset{-1}{\circ}\!\!\!\textsf{|||||}\!\!\underset{5}{\circ}\!\!\overset{*****~~~}{\textsf{|||}}\!\!\!\footnotesize\begin{array}{l}\blacktriangleright \end{array}\qquad \mathbb{R}}\\\\ \mathsf{r>-1}&\qquad\mathsf{\textsf{|||}\!\!\!\underset{-1}{\circ}\!\!\!\overset{********************~~~}{\textsf{|||||}\!\!\underset{5}{\bullet}\!\!\textsf{|||}}\!\!\!\footnotesize\begin{array}{l}\blacktriangleright \end{array}\qquad \mathbb{R}}\\\\\\ \mathsf{r>5~~or~~r>-1}&\qquad\mathsf{\textsf{|||}\!\!\!\underset{-1}{\circ}\!\!\!\overset{********************~~~}{\textsf{|||||}\!\!\underset{5}{\bullet}\!\!\textsf{|||}}\!\!\!\footnotesize\begin{array}{l}\blacktriangleright \end{array}\qquad \mathbb{R}} \end{array}$

The result is found just by joining those two intervals together. Actually that compound inequality only implies

r > – 1

which does not represent all real numbers.

—————

B) r > 5 or r < – 1.

$\large\begin{array}{cl} \mathsf{r>5}&\qquad\mathsf{\textsf{|||}\!\!\!\underset{-1}{\circ}\!\!\!\textsf{|||||}\!\!\underset{5}{\circ}\!\!\overset{*****~~~}{\textsf{|||}}\!\!\!\footnotesize\begin{array}{l}\blacktriangleright \end{array}\qquad \mathbb{R}}\\\\ \mathsf{r5~~or~~r$

Numbers between – 1 and 5 (including them) are not included in the union, so you don't have all real numbers represented there either.

—————

C) r < 5 or r < – 1.

$\large\begin{array}{cl} \mathsf{r$

Numbers that are greater or equal to 5 are not in the union. So it does not represent all real numbers.

—————

D) r < 5 or r > – 1.

$\large\begin{array}{cl} \mathsf{r-1}&\qquad\mathsf{\textsf{|||}\!\!\!\underset{-1}{\circ}\!\!\!\overset{********************~~~}{\textsf{|||||}\!\!\underset{5}{\bullet}\!\!\textsf{|||}}\!\!\!\footnotesize\begin{array}{l}\blacktriangleright \end{array}\qquad \mathbb{R}}\\\\\\ \mathsf{r-1}&\qquad\mathsf{\overset{~~~**************************~~~}{\textsf{|||}\!\!\!\underset{-1}{\bullet}\!\!\!\textsf{|||||}\!\!\underset{5}{\bullet}\!\!\textsf{|||}}\!\!\!\footnotesize\begin{array}{l}\blacktriangleright \end{array}\qquad \mathbb{R}} \end{array}$

Now all real numbers are included in the union. So this is the right choice.

Answer: option D) r < 5 or r > – 1.

I hope this helps. =)

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3 years ago