Given:
The line parallel to the given line containing the points (-3,3) and (-2,1).
Also, the parallel line passes through the point (4,1).
We need to determine the equation of the line in slope - intercept form.
Slope:
Since, the two lines are parallel, then their slopes are equal.
Thus, the slope of the parallel line can be determined using the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substituting the points (-3,3) and (-2,1), we get;
[tex]m=\frac{1-3}{-2+3}[/tex]
[tex]m=\frac{-2}{1}[/tex]
[tex]m=-2[/tex]
Thus, the slope of the line is [tex]m=-2[/tex]
Equation of the line:
The equation of the line can be determined using the formula,
[tex]y-y_1=m(x-x_1)[/tex]
Since, the line passes through the point (4,1), let us substitute the point (4,1) in the above formula, we have;
[tex]y-1=-2(x-4)[/tex]
Thus, the equation of the line is [tex]y-1=-2(x-4)[/tex]
Hence, Option a is the correct answer.
We know that two lines are parallel if they have the same slope.
Using this, we will find that the line parallel to the one graphed and that passes through (4, 1) is: y = -2*x + 9
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Let's see how we can find the line:
To find the line, the first thing we need to do is find the slope of the graphed line.
Remember that a general line is something like:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we do know that the line passes through the points (x₁, y₁) and (x₂, y₂) then the slope of that line can be written as:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here we can see that the graphed line passes through (-3, 3) and (-2, 1). Then the slope will be:
[tex]a = \frac{1 - 3}{2 - (-3)} = \frac{-2}{1} = -2[/tex]
Then the slope of the parallel line is also -2, so the parallel line will be something like:
y = -2*x + c
To find the value of c, we use the fact that this line passes through (4, 1).
So when x = 4, we must have y = 1.
Repacing these in the line equation we get:
1 = -2*4 + c
1 = -8 + c
1 + 8 = c = 9
Then the parallel line to the graphed one that passes through (4, 1) is:
y = -2*x + 9
If you want to learn more, you can read:
https://brainly.com/question/2263981
