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Marina86 [1]
3 years ago
15

A line is graphed below. Write an equation in the form y = mx + b that represents this line

Mathematics
1 answer:
galben [10]3 years ago
3 0
<h3><u>Explanation</u></h3>
  • Slope-Intercept form

y = mx + b \\ m = slope \\ b = y - intercept

  • Calculate the slope with two given coordinate by using rise over run.

\begin{cases}(x_1,y_1) = ( - 4,0) \\ (x_2,y_2) = ( 0,2) \end{cases}

These two coordinate points are part of the graph and can be used to find the slope.

m =  \frac{y_2 -y_1 }{x_2 -  x_1}

Substitute the coordinate points in the formula.

m  =  \frac{2 - 0}{0 - ( - 4)}  \\ m =  \frac{2}{ 4}  \\ m =  \frac{1}{2}

Therefore, the slope is 2.

Rewrite the equation in slope-intercept.

y =  \frac{1}{2} x + b

  • Calculate the y-intercept by substituting any given points in new rewritten equation.

(x,y) = ( 0,2)

I will be substituting these coordinate points in the equation.

y =  \frac{1}{2} x + b

Substitute x = 0 and y = 5 in the equation.

2 =  \frac{1}{2} (0) + b \\ 2 = 0 + b \\ 2 = b

Therefore the y-intercept is (0,2).

Rewrite the equation.

y =  \frac{1}{2} x + 2

<h3><u>Answer</u></h3>

<u>\large \boxed{y =  \frac{1}{2} x + 2}</u>

<em>If</em><em> </em><em>you</em><em> </em><em>have</em><em> </em><em>any</em><em> </em><em>questions</em><em> </em><em>related</em><em> </em><em>to </em><em>the</em><em> </em><em>answer</em><em>,</em><em> </em><em>feel</em><em> </em><em>free to</em><em> </em><em>ask me</em><em> </em><em>via</em><em> </em><em>comment</em><em>.</em><em> </em>

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If the 12 miles had been all level, it would have taken approximately 3 hours. It the 12 miles had been all uphill, it would have taken approximately 4 hours. When reaching the peak, 3.5 hours would have been the approximate time it took them to reach the top since it is in between. <span />
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3 years ago
Let a and b be roots of x² - 4x + 2 = 0. find the value of a/b² +b/a²​
erastovalidia [21]

Answer:

\dfrac{a}{b^2}+\dfrac{b}{a^2}=10

Step-by-step explanation:

Given equation:   x^2-4x+2=0

The roots of the given quadratic equation are the values of x when y=0.

To find the roots, use the quadratic formula:

x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0

Therefore:

a=1, \quad b=-4, \quad c=2

\begin{aligned}\implies x & =\dfrac{-(-4) \pm \sqrt{(-4)^2-4(1)(2)}}{2(1)}\\& =\dfrac{4 \pm \sqrt{8}}{2}\\& =\dfrac{4 \pm 2\sqrt{2}}{2}\\& =2 \pm \sqrt{2}\end{aligned}

\textsf{Let }a=2+\sqrt{2}

\textsf{Let }b=2-\sqrt{2}

Therefore:

\begin{aligned}\implies \dfrac{a}{b^2}+\dfrac{b}{a^2} & = \dfrac{2+\sqrt{2}}{(2-\sqrt{2})^2}+\dfrac{2-\sqrt{2}}{(2+\sqrt{2})^2}\\\\& = \dfrac{2+\sqrt{2}}{6-4\sqrt{2}}+\dfrac{2-\sqrt{2}}{6+4\sqrt{2}}\\\\& = \dfrac{(2+\sqrt{2})(6+4\sqrt{2})+(2-\sqrt{2})(6-4\sqrt{2})}{(6-4\sqrt{2})(6+4\sqrt{2})}\\\\& = \dfrac{12+8\sqrt{2}+6\sqrt{2}+8+12-8\sqrt{2}-6\sqrt{2}+8}{36+24\sqrt{2}-24\sqrt{2}-32}\\\\& = \dfrac{40}{4}\\\\& = 10\end{aligned}

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Answer quick for brainliest
Alenkasestr [34]

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Step-by-step explanation:

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Please help me with this
kondaur [170]
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7:26 or
\frac{7}{26}
For number 2a. the answer is 8 to 28 or
8:28 or
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For number 3a. the answer is 12 to 13 or
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\frac{12}{13}
For number 4a. the answer is 19 to 12 or
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\frac{19}{12}
For number 5a. the answer is 29 to 10 or
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\frac{29}{10}
For number 6a. the answer is 11 to 28 or
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\frac{11}{28}

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