What is the equation of the line passing through (1, 7) and parallel to the line y = –x + 5 in standard form?
To find the equation of a line parallel to another line, we need to use the fact that parallel lines have the same slope. In this case, the given line has a slope of -1.
We can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept. Since we have the slope (-1) and a point (1, 7) on the line, we can substitute these values into the equation to find the value of b.
Substituting the values, we get 7 = -1(1) + b.
Simplifying further, 7 = -1 + b.
Adding 1 to both sides, we get 8 = b.
Now that we have the values of m and b, we can substitute them into the standard form of a line, Ax + By = C, where A, B, and C are constants.
Substituting, we get -1x + 1y = 8.
Simplifying, we get -x + y = 8.
So the equation of the line passing through (1, 7) and parallel to the line y = –x + 5 in standard form is -x + y = 8.