Find the equation of the line that is parallel to the line y = -4x + 8 and passes through the point (6, -9). Write the equation in point-slope form.
Find the equation of the line that is parallel to the line y = -4x + 8 and passes through the point (6, -9). Write the equation in point-slope form
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To find the equation of a line that is parallel to the line (y = -4x + 8) and passes through the point ((6, -9)), we can follow these steps:
1. Identify the slope: The slope of the given line (y = -4x + 8) is (-4). Since parallel lines have the same slope, the slope of our new line will also be (-4).
2. Use the point-slope form of a line: The point-slope form is given by the equation:
[
y – y_1 = m(x – x_1)
]
where ((x_1, y_1)) is a point on the line and (m) is the slope.
3. Plug in the values: Using the point ((6, -9)) and the slope (-4):
[
y – (-9) = -4(x – 6)
]
Simplifying this gives:
[
y + 9 = -4(x – 6)
]
4. Final equation: Therefore, the equation of the line in point-slope form is:
[
y + 9 = -4(x – 6)
]
This equation represents the line you are looking for! If you need any further assistance or in-depth explanations, feel