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Explanation:
To write the point-slope form of the equation of a line, we need the coordinates of a point on the line and the slope of the line. Given the point and the fact that the line is parallel to another line, we can find the slope of the line.Let's determine the slope of the given parallel lines and use it to write the equations in point-slope form:Given line: through (4, 2), parallel to y = -5xSince the given line is in the form y = mx, we can identify the slope of the line as m = -5. Using this slope and the given point (4, 2), we can write the equation in point-slope form:y - y1 = m(x - x1)
y - 2 = -5(x - 4)Given line: through (-3, -3), parallel to y = -5xUsing the same slope, m = -5, and the given point (-3, -3), we can write the equation in point-slope form:y - y1 = m(x - x1)
y - (-3) = -5(x - (-3))Given line: through (-4, 0), parallel to y = -x - 4The given line has a slope of -1. Therefore, the parallel line will also have a slope of -1. Using the given point (-4, 0), we can write the equation in point-slope form:y - y1 = m(x - x1)
y - 0 = -1(x - (-4))Given line: through (-1, 4), parallel to y = -5x + 2The given line has a slope of -5. The parallel line will have the same slope. Using the given point (-1, 4), we can write the equation in point-slope form:y - y1 = m(x - x1)
y - 4 = -5(x - (-1))Given line: through (2, 0), parallel to y = 3x + 3The given line has a slope of 3. The parallel line will also have a slope of 3. Using the given point (2, 0), we can write the equation in point-slope form:y - y1 = m(x - x1)
y - 0 = 3(x - 2)Given line: through (4, -4), parallel to y = -x - 4The given line has a slope of -1. The parallel line will have the same slope. Using the given point (4, -4), we can write the equation in point-slope form:y - y1 = m(x - x1)
y - (-4) = -1(x - 4)Given line: through (-2, 4), parallel to y = -5xThe given line has a slope of -5. The parallel line will have the same slope. Using the given point (-2, 4), we can write the equation in point-slope form:y - y1 = m(x - x1)
y - 4 = -5(x - (-2))Given line: through (-4, -1), parallel to y = -3x - 2The given line has a slope of -3. The parallel line will have the same slope. Using the given point (-4, -1), we can write the equation in point-slope form:y - y1 = m(x - x1)
y - (-1) = -3(x - (-4))Note