Question

Line v passes through point (6, 6) and is perpendicular to the graph of y = 34x – 11. Line w is parallel to line v and passes through point (–6, 10). Which is the equation of line w in slope-intercept form?

Answer 1

Two parallel lines have the same slope. If line w is perp. to y = 34x - 11, we must find the slope of y = 34x - 11 and then find the negative reciprocal of that slope. That (neg. recip.) slope will be the slope of line w.

The slope of y = 34x - 11 is 34, and the neg recip. of that is -1/34: slope of w.

Use the point-slope form of the equation of a str. line to find the eqn. of line w:

y - 10 = (-1/34)*(x - (-6) ) => y - 10 = (-1/34)(x+6). This could be rewritten in other forms if desired.

Answer 2

y = -1/34 . x + 167/17

Explanation:

The slope-intercept form of a linear equation is:

y = m.x + b

where,

m is the slope

b is the y-intercept

Line v is perpendicular to the graph of y = 34 x - 11. If 2 lines are perpendicular, the slope of one is the inverse and opposite of the other. Then, the slope of v is -1/34.

Line w is parallel to line v. When 2 lines are parallel, they have the same slope.

The equation of w is:

y = -1/34 . x + b

Lines b passes through the point (-6, 10). We can replace this ordered pair in the previous equation to find the value of b.

10 = -1/34 . (-6) + b

b = 167/17

The equation of w is:

y = -1/34 . x + 167/17