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What is the slope of a trend line that passes through the points [tex][tex]$(-3,3)$[/tex][/tex] and [tex][tex]$(18,26)$[/tex][/tex]?

A. [tex][tex]$\frac{15}{29}$[/tex][/tex]
B. [tex][tex]$\frac{21}{23}$[/tex][/tex]
C. [tex][tex]$\frac{23}{21}$[/tex][/tex]
D. [tex][tex]$\frac{29}{15}$[/tex][/tex]


Sagot :

To find the slope of a line that passes through two points, we use the slope formula:

[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

where [tex]\((x_1, y_1) = (-3, 3)\)[/tex] and [tex]\((x_2, y_2) = (18, 26)\)[/tex].

First, we calculate the change in [tex]\(y\)[/tex] (delta [tex]\(y\)[/tex]):

[tex]\[ \Delta y = y_2 - y_1 = 26 - 3 = 23 \][/tex]

Next, we calculate the change in [tex]\(x\)[/tex] (delta [tex]\(x\)[/tex]):

[tex]\[ \Delta x = x_2 - x_1 = 18 - (-3) = 18 + 3 = 21 \][/tex]

Now, we substitute these values into the slope formula:

[tex]\[ m = \frac{\Delta y}{\Delta x} = \frac{23}{21} \][/tex]

Therefore, the slope of the line that passes through the points [tex]\((-3, 3)\)[/tex] and [tex]\(18, 26)\)[/tex] is:

[tex]\[ \boxed{\frac{23}{21}} \][/tex]
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