its C because −1, 2) and (3, 4)
The slope (rise/run) is m = (4 − 2)/(3 − (−1)= 2/4
2/4 = 1/2
y − y1 = m(x − x1)
y − 4 = 12(x − 3)
y = 1/2x + 5/2
We want to find a line equation given that we know that the line passes through two known points.
The correct option is C, we will get the line:
[tex]y = \frac{1}{2}*x + \frac{5}{2}[/tex]
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A general line in the slope-intercept form can be written as:
[tex]y = a*x + b[/tex]
Where a is the slope and b is the y-intercept.
We know that if the line passes through two points (x₁, y₁) and (x₂, y₂) the slope can be written as:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here we do know that our line passes through (-1, 2) and (3, 4) then the slope will be:
[tex]a = \frac{4 - 2}{3 - (-1)} = \frac{2}{4} = \frac{1}{2}[/tex]
Then the line is something like:
[tex]y = \frac{1}{2}*x + b[/tex]
To find the value of b, we can use the fact that the line passes through one of the given points, for example we can use (-1, 2).
This means that when x= -1, we must have y = 2.
Then we can replace these in the above equation to get:
[tex]2 = \frac{1}{2}*(-1) + b \\2 + \frac{1}{2} = b\\\frac{5}{2} = b[/tex]
Then the line equation is:
[tex]y = \frac{1}{2}*x + \frac{5}{2}[/tex]
So the correct option is C.
If you want to learn more, you can read:
https://brainly.com/question/20632687
