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ian2006huang
24.06.2021 •
Mathematics
okay so i know the slope is 3/5. but is there any easier way for me to find out the points that fall on p?
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Ответ:
Step-by-step explanation:
There is! Algebraically, we can find the equation of the line. Any points that the line passes through should make the equation of the line true.
In slope-intercept form, the equation of a line is given by
, where
is the slope of the line,
is the y-intercept, and
represents any point the line passes through.
The slope of a line is given by the change in y-values over the change in x-values of two points the line passes through. We're given that the line passes through the points (-6, -4) and (-3, 1).
Let:
The slope of the line that passes through these points is![m=\frac{y_2-y_1}{x_2-x_1}=\frac{1-(-4)}{-3-(-6)}=\frac{5}{3}](/tpl/images/1382/8334/5bab4.png)
Now substitute
and any point (x, y) that the line passes through to solve for
in
:
Using (-3, 1):
Thus, the equation of the line is
.
I just realized that it's asking for the points that the line parallel to this line and passing through point
goes through, but I'll keep all the information above as it may be useful.
Parallel lines always have equal slopes, by definition. Therefore, the slope of the line that passes through point
and is parallel to the line above also has a slope of
. Point
is located at (3, -2). Thus, to find
, plug in
and
into
:
Therefore, the equation of this line must be
.
You can algebraically determine if a certain point passes through this line by seeing if the point makes this equation true. From the answer choices, the following points are passed through by this line:
Ответ:
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