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starrhunter
What is the equation of the line that passes through the point (4, 1) and is perpendicular to the line y = –2x + 4?
Do you know point-slope form of the equation of a line?
no i dont know any algebra im trying to help my sister finish her assignments. shes in the hospital. i dont need anyone to teach me anything i just dont want her to fail. any good answers anyone has is greatly appreciated
Sorry. It is contrary to the code of conduct to just post answers. Too many kids try to avoid learning that way.
could u show me how to work it out then? dont want anyone to get in trouble.
\[y-y _{1}=m(x-x _{1})\]
First, determine the slope of the given line. x + 2y = 6 Solve for y to get this in slope-intercept form. Remember to switch signs when you switch sides. 2y = -x + 6 Divide all terms on both sides by 2. y = -0.5 x + 3 So the slope of the given line is the coefficient of x, which is -0.5 = -1/2 The slope of a perpendicular line is the negative reciprocal of that slope, which would be 2. Use the point-slope form to build the equation with the point (4,2) y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. y - 2 = 2(x - 4) This is an equation that satisfies the question. To get this into slope-intercept form, expand, simplify and solve for y. y = 2x - 8 + 2 y = 2x - 6
That is point-slope form. The given line has slope -2 so the perpendicular has slope 1/2 replace y1with 1, m with 1/2 and x1 with 4 and simplify. That will be the equation of the desired line.
Yep, take it with a little grain of salt
so what do i have to simplify exactly?
and make y the subject of the formula
To simplify, distribute the 1/2 and then add 1 to both sides.