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GuDViN [60]
3 years ago
7

A line contains the points (-3, 4) and (7, -1). Calculate the equation of the line in the form y = mx + b Explain each step.

Mathematics
2 answers:
andre [41]3 years ago
6 0

\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-4}{7-(-3)}\implies \cfrac{-5}{7+3}\implies \cfrac{-5}{10}\implies -\cfrac{1}{2}

\bf \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-4=-\cfrac{1}{2}[x-(-3)]\implies y-4=-\cfrac{1}{2}(x+3) \\\\\\ y-4=-\cfrac{1}{2}x-\cfrac{3}{2}\implies y=-\cfrac{1}{2}x-\cfrac{3}{2}+4\implies y=-\cfrac{1}{2}x+\cfrac{5}{2}

Daniel [21]3 years ago
3 0
In order to find the equation of the line, you must first find the gradient of the line

Gradient of a line (m)= (y2-y1)/(x2-x1)
.....Now you substitute the points...
= ((-1)-4)/(7-(-3))
= (-5)/(10)
= -1/2

Therefore the gradient is negative a half (-1/2)

Now we can find the equation of the line. You can use one of the two points to find the equation of the line

Equation of a line: y-y1=m(x-x1)
... I chose to use (7,-1) as my points....
y-(-1)=-1/2(x-7)
y+1=-x/2+7/2
y=-x/2+(7/2)-1
1) y=-x/2+5/2
..... if you would like you can multiply everything by 2 to have while numbers instead of fractions ....
2) 2y=-x+5
... if you are uncomfortable of having x as negative, you can transpose it carrying both the -x and the 5 to the side of the 2y. NOTE that the sign changes and the equation will be equal to 0....
3) 2y+x-5=0

1,2 and 3 are all correct answers, just in different forms

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the scale factor used in Emily scale drawing is K = 1.63 mm/m

<h3>What scale did Emily use?</h3>

We know that Emily drew a scale drawing of a house and its lot.

In the scale drawing, the back patio is 42 millimeters long, and we know that the actual patio is 27 meters long.

Then the scale relates the measures 44mm and 27 meters, such that if the scale is K, we can write:

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If you want to learn more about scale factors:

brainly.com/question/25722260

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Help i dont ge it show work how do you solve it,???
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