Question

In Exercises 3 and 4, write an equation of the line passing through point P that is parallel to the given line y = 4x - 7. What is the equation of the line passing through point P (-1, 3)?

A) y = 4x - 7
B) y = 4x - 4
C) y = 3x - 6
D) y = 3x - 4

Answer 1

To find the equation of a line parallel to y = 4x - 7 passing through point P (-1, 3), we need to use the fact that parallel lines have the same slope. The equation of the line passing through P is y - 3 = 4(x - (-1)). Substituting -3 for y and -1 for x, we get -3 - 3 = 4(-1 + 1), which simplifies to -6 = 0, indicating that there is no equation.

Step-by-step explanation:

To find the equation of a line parallel to y = 4x - 7 passing through point P (-1, 3), we need to use the fact that parallel lines have the same slope. The given line has a slope of 4, so the parallel line will also have a slope of 4. Using the point-slope form of a linear equation, the equation of the line passing through P is y - 3 = 4(x - (-1)). Simplifying, we get y - 3 = 4(x + 1). Substituting -3 for y and -1 for x, we get -3 - 3 = 4(-1 + 1). This simplifies to -6 = 0, which is not a true statement. Therefore, the equation of the line passing through P (-1, 3) parallel to y = 4x - 7 is there is no equation.