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Write the point-slope form of the equation of the line that passes through the points (-3, 5) and (-1, 4). Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.

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bunnymarshmarloykw47
Firstly, we need to understand the formula of point-slope form:
[tex]y1 - y2 =m( x1 - x2)[/tex]

Where x and y is the coordinates and m is the slope respectively.

To find the slope:
[tex] \frac{y1 - y2}{x1 - x2} [/tex]
In this case:
[tex] \frac{5 - 4}{ - 3 - ( - 1)} \\ = \frac{1}{ - 3 + 1} \\ = - \frac{1}{2} [/tex]

We can then put the above slope and the point (-1,4) into the formula:

4-y = -1/2(-1-x)
-y = 1/2+1/2x-4
y = -1/2x+7/2

Alternatively:

y-4=-1/2(x-(-1))
y=-1/2x-1/2+4
y = -1/2x+7/2

Therefore the answer is y = -1/2x+7/2.

Hope it helps!
peachimin

answer:  [tex]y = -\frac{1}{2}x + \frac{7}{2}[/tex]  

work/explanation:

point slope formula ==> [tex]y - y_{1} = m(x - x_{1})[/tex]  | plug the points

slope formula ==> [tex]m =\frac{y_{2} - y_{1}}{x_{2}-x_{1}}[/tex] | for slope or m

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first you find the slope of the lines.

[tex]m =\frac{4-5}{-1-3 } = -\frac{1}{2}[/tex]  <== slope or m for the equation

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plug the points and slope into the point-slope formula.

[tex]y - 4 = -\frac{1}{2} (x - -3)[/tex]


solve the equation until the answer is [tex]y =mx + b[/tex] form.

[tex]y - 4 = -\frac{1}{2} (x + 3)[/tex]  | multiply -1/2 into the parentheses

[tex]y -4 = -\frac{1}{2}x - \frac{1}{2}[/tex]  | add the 4, move it over to -1/2

[tex]y = -\frac{1}{2}x + \frac{7}{2}[/tex]  | final answer :)

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hope this helps! i'm sorry i took a while to answer ❤ from peachimin

EDIT: i put in the correct numbers




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