Question

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.

Answer 1

Firstly, we need to understand the formula of point-slope form:
$y1 - y2 =m( x1 - x2)$

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

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

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!

Answer 2

answer:  $y = -\frac{1}{2}x + \frac{7}{2}$  

work/explanation:

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

slope formula ==> $m =\frac{y_{2} - y_{1}}{x_{2}-x_{1}}$ | for slope or m

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first you find the slope of the lines.

$m =\frac{4-5}{-1-3 } = -\frac{1}{2}$  <== slope or m for the equation

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

$y - 4 = -\frac{1}{2} (x - -3)$

solve the equation until the answer is $y =mx + b$ form.

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

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

$y = -\frac{1}{2}x + \frac{7}{2}$  | 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