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3 years ago

What is an equation of the line that passes through the points (4,-6) and has a slope of -3

Mathematics

1 answer:

Akimi4 [234]3 years ago

7 0

Answer:

1) y = -3x + 6

Step-by-step explanation:

1) First, write the equation of the line in point-slope form with the given information. Use the point-slope formula $y-y_1 = m (x-x_1)$ and substitute values for $m$ , $x_1$ , and $y_1$ .

Since $m$ represents the slope, substitute -3 in its place. Since $x_1$ and $y_1$ represent the x and y values of the point the line intersects, substitute the x and y values of (4,-6) into the formula as well. This gives the following equation:

$y+6 = -3(x-4)$

2) Now, isolate the y in the equation to put it in slope-intercept form and find the answer.

$y + 6 = -3(x-4)\\y + 6 = -3x+12\\y = -3x+6$

So, the first option is correct.

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A compound inequality for the graph would be:

x >= 0 and x < 2

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4 years ago

What is the standard form of the linear function that passes

babunello [35]

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$(\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{4}}}\implies \cfrac{-3}{-2}\implies \cfrac{3}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{\cfrac{3}{2}}(x-\stackrel{x_1}{4})$

$\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2(y-1)=2\left( \cfrac{3}{2}(x-4) \right)}\implies 2y-2 = 3(x-4)\implies 2y-2=3x-12 \\\\\\ -3x+2y-2=-12\implies -3x+2y=-10\implies \stackrel{\times -1\textit{ to both sides}}{3x-2y=10}$

7 0

2 years ago

2 tens plus 13 ones

Anton [14]

Hello from MrBillDoesMath!

Answer:

Discussion:

2 tens = 2 * 10 = 20

13 ones = 13 * 1 13

=> 2 tens + 13 ones = 20 + 13 = 33

Thank you,

MrB

3 0

3 years ago

Read 2 more answers

The sum of two numbers is 47 and the difference is 25 . what are the numbers?

taurus [48]

The numbers are: 36 and 11 .
______________________________________________
Explanation:
______________________________________________
Let us represent the TWO (2) numbers with the variables;
         "x" and "y" .
__________________________________________
     x + y = 47 .

     y − x = 25.
__________________________________________
Since: " y − x = 25 " ;

Solve for "y" in terms of "x" ;

y − x = 25 ;

Add "x" to each side of the equation:
_____________________________________________
   y − x + x = 25 + x ;

to get:

   y = 25 + x .

Now, since:

x + y = 47 ;

Plug in "(25 + x)" as a substitution for "y"; to solve for "x" :

x + (25 + x) = 47 ;

x + 25 + x + 47 ;

2x + 25 = 47 ;

Subtract "25" from each side of the equation:

2x + 25 − 25 = 47 − 25 ;

2x = 22 ;

Divide EACH SIDE of the equation by "2" ;
to isolate "x" on one side of the equation; and to solve for "x" ;

2x / 2 = 22 / 2 ;

    x = 11 ;
______________________________________________
x + y = 47<span> ;

</span>Plug in "11" for "x" into the equation ; to solve for "y" ;

11 + y = 47 ;

Subtract "11" from EACH SIDE of the equation;
to isolate "y" on one side of the equation; and to solve for "y" ;

11 + y − 11 = 47 − 11 ;

            y = 36 .
___________________________________________
So: x = 11 , y = 36 ;
___________________________________________
Let us check our work:

y − x = 25 ;

36 − 11 =? 25 ? Yes!

x + y = 47 ;

36 + 11 =? 47 ? Yes!
______________________________________________
The numbers are: 36 and 11 .
______________________________________________

5 0

3 years ago

Pherris is graphing the function f(x) = 2(3)x. He begins with the point (1, 6). Which could be the next point on his graph?

Savatey [412]

Answer: (2, 18)

Step-by-step explanation:

When x=2, $f(2)=2(3)^{2}=18$ .

So, it should pass through (2, 18).

8 0

2 years ago