Question

Write an equation in slope-intercept form for the line described. Write the slope and y-intercept as fractions, if necessary. The line passes through the point (6, 2) and is parallel to the line y = -x + 1.

Answer 1

The equation of the line passing through the point (6, 2) and parallel to the line y = -x + 1 is y = -x + 8.

Step-by-step explanation:

The line y = -x + 1 is in slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the slope is -1 and the y-intercept is 1. Since the line we want to find is parallel to this line, it will have the same slope. So the slope of the new line is -1.

Given that the point (6, 2) lies on the line, we can substitute the values of x and y into the equation y = mx + b to solve for b.

2 = -1 * 6 + b

2 = -6 + b

b = 8

Therefore, the equation of the line passing through the point (6, 2) and parallel to the line y = -x + 1 is y = -x + 8.