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.
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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.
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