What is the equation in point-slope form for the line parallel to y = 5x – 4 that contains P(-6, 1)? Select one: a. x – 1 = -5(y + 6) b. y + 1 = 5(x + 6) c. y – 1 = -5(x + 6) d. y – 1 = 5(x + 6) PLS HELP
The Correct Answer and Explanation is:
To find the equation of a line that is parallel to y=5x−4y = 5x – 4y=5x−4 and passes through the point P(−6,1)P(-6, 1)P(−6,1), we need to first understand the following steps:
Step 1: Identify the slope of the given line
The equation of the line is y=5x−4y = 5x – 4y=5x−4, which is in slope-intercept form (y=mx+by = mx + by=mx+b), where mmm represents the slope. From the equation, the slope is m=5m = 5m=5.
Step 2: Recognize that parallel lines have the same slope
Since the line we are looking for is parallel to the given line, it will have the same slope, which is m=5m = 5m=5.
Step 3: Use the point-slope form of the line equation
The point-slope form of the equation for a line is given by:y−y1=m(x−x1)y – y_1 = m(x – x_1)y−y1=m(x−x1)
where mmm is the slope of the line, and (x1,y1)(x_1, y_1)(x1,y1) is the point through which the line passes. In this case, we know the slope m=5m = 5m=5 and the point P(−6,1)P(-6, 1)P(−6,1), where x1=−6x_1 = -6×1=−6 and y1=1y_1 = 1y1=1.
Step 4: Substitute the values into the point-slope form
Substituting the slope m=5m = 5m=5 and the coordinates of point P(−6,1)P(-6, 1)P(−6,1) into the formula, we get:y−1=5(x+6)y – 1 = 5(x + 6)y−1=5(x+6)
Step 5: Choose the correct option
The equation we derived, y−1=5(x+6)y – 1 = 5(x + 6)y−1=5(x+6), matches option d.
Conclusion:
The correct equation of the line in point-slope form is d. y−1=5(x+6)y – 1 = 5(x + 6)y−1=5(x+6). This equation represents the line parallel to y=5x−4y = 5x – 4y=5x−4 and passing through P(−6,1)P(-6, 1)P(−6,1).
