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Write an equation of a line that goes through point (4, −5) and is parallel to line y = -3x + 8. Show all work.
To find the equation of a line that is parallel to a given line, we need to use the fact that parallel lines have the same slope.
Given the equation of the given line is y = -3x + 8, we can determine its slope by comparing it to the standard form equation y = mx + b, where m is the slope.
From the given equation, we can see that the slope of the given line is -3.
Since our parallel line should have the same slope, the slope of our parallel line is also -3.
Now, we can substitute the slope and the coordinates of the given point (4,-5) into the point-slope form of a linear equation to find the equation of the line.
The point-slope form is given by: y - y₁ = m(x - x₁)
Substituting the values, we have:
y - (-5) = -3(x - 4)
Simplifying the equation:
y + 5 = -3(x - 4)
Expanding and rearranging the equation:
y + 5 = -3x + 12
Subtracting 5 from both sides:
y = -3x + 7
Therefore, the equation of the line that goes through the point (4,-5) and is parallel to the line y = -3x + 8 is y = -3x + 7.
To find the equation of a line parallel to y = -3x + 8 and passing through the point (4, -5), we will use the fact that parallel lines have the same slope.
The given line y = -3x + 8 is in slope-intercept form y = mx + b, where m is the slope.
Therefore, the slope of the given line is -3.
Since the line we want to find is parallel, it will have the same slope of -3.
Now we can use the point-slope form of a linear equation to find the equation of the line.
The point-slope form is given by y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope.
Plugging in the given values, the equation becomes:
y - (-5) = -3(x - 4)
Simplifying the equation:
y + 5 = -3x + 12
Subtracting 5 from both sides:
y = -3x + 7
So, the equation of the line that goes through the point (4, -5) and is parallel to the line y = -3x + 8 is y = -3x + 7.
To write an equation of a line that is parallel to the given line, we need to use the same slope as the given line. The slope of the given line is -3.
So, the equation of the line we are looking for can be written in the form y = mx + b, where m is the slope and b is the y-intercept.
We already know the slope is -3, so let's plug it in: y = -3x + b.
To find the value of b, we need to use the coordinates of the given point (4, -5). We can substitute these values into the equation and solve for b.
Using the coordinates (4, -5), we have:
-5 = -3(4) + b
Simplifying the equation:
-5 = -12 + b
b = -5 + 12
b = 7
Now that we have the value of b, we can rewrite the equation of the line:
y = -3x + 7
Therefore, the equation of the line that goes through point (4, -5) and is parallel to the line y = -3x + 8 is y = -3x + 7.