Point t slope form: y + y value = m (x + x value) where m is the gradient Parallel line must have the same gradient as the two lines never meet, so the gradient must be 4. This eliminates option B and D. Remember that point-slope form is still an equation, so the values of both sides must be equal. So let's substitute the given coordinates. Option A: y-6=4(x+2) -6-6 (-12) does not equal to 4(-2+2) (0) Option C: y+6=4(-2+2) -6+6 (0) = 4(-2+2) (0) Therefore, option C is your answer.
- Point slope form is y - b = m(x - a), where m is the slope and (a, b) is a point on the line. - Parallel lines have the same slope
The given equation is in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. m in y = 4x - 14 is 4; our equation in point-slope form will have 4 as m. We have the slope (4), so now we have to add the "point on the line" which is given: P(-2, -6). That's all the information needed to write an equation in point-slope form that's parallel to y = 4x - 14; all that's left is to substitute and simplify.
y - b = m(x - a) y - (-6) = 4(x - (-2)) y + 6 = 4(x + 2)
This is because to get to 14/15 you must divide by 6 but when getting to 42/45 you must divide 2. Therefore 14/15 is your answer because the problem went to the most reduced fraction.
