What is the equation of the line in standard form that passes through the point (3, –2) and is parallel to the line y = –4x + 1?

Question

parthkohli · Answer

You know the point and the slope, so the point-slope form:$$y - y_0 = m(x - x_0)$$

anonymous · Answer

Parallel means   Slopes are equal ie m1 = m2

parthkohli · Answer

Now the points you have are $(x_0, y_0)$ and $m$ is the slope.

anonymous · Answer

y = mx + c

m = slope

parthkohli · Answer

As @Yahoo! said, the slope will be equal.$$y - y_0 = -4(x - x_0)$$Now your point.

parthkohli · Answer

Hello?

anonymous · Answer

Oooook so what your saying is the equation would be .. y-2=m(x-3)  ??

anonymous · Answer

Im sorry guys, im lost with this stuff..

whpalmer4 · Answer

Okay, I'll start from the top:  parallel lines have the same slope.  We know the slope of the other line (y = -4x + 1) to be m = -4, because it is in slope-intercept form (y = mx + b).  So, our line will also have slope m = -4.  Because we know a point our line passes through, and we know the slope, point-slope form is the most convenient.  Our known point is (x0, y0) = (3, -2) and point-slope form for a line is 
$$y-y_0 = m(x-x_0)$$ so plugging in what we know, we get
$$y-(-2) = -4(x-3)$$$$y+2 = -4x +12\rightarrow y = -4x + 10$$Now, the problem asks for us to put the formula in standard form, which is Ax + By = C, with neither A nor B = 0.  So, we add -4x to both sides giving us x and y terms on the left and a constant on the right, which is standard form.  What is your answer?

whpalmer4 · Answer

Sorry, we add 4x, not -4x!

anonymous · Answer

Ok so i almost got it, Except for...
 the problem asks for us to put the formula in standard form, which is Ax + By = C, with neither A nor B = 0.  So, we add -4x to both sides giving us x and y terms on the left and a constant on the right, which is standard form.
I dont understand the Ax+By=C part..

whpalmer4 · Answer

It means you need to have x and y on the left side of the equals sign, and a number on the right.  A and B are constants, and they can't equal 0.

whpalmer4 · Answer

C is a constant, too.  It can equal 0.  Except in this problem, it doesn't :-)

whpalmer4 · Answer

$$y = -4x + 10$$We need both x and y on the left side, so we add 4x to each side:
$$y + 4x = -4x + 10 + 4x$$$$y +4x = 10$$Voilà, our equation in standard form!

whpalmer4 · Answer

Here's a diagram showing the original line (in blue) and our new, parallel line passing through (3, -2) in purple.

anonymous · Answer

Ok so im still kinda confused lol im so sorry, math is like greek to me..

anonymous · Answer

OH! the graph is very helpful, thank you

whpalmer4 · Answer

Millions of Greek kids learn Greek, you can do it too :-)

anonymous · Answer

Lol.. i think i should conquer algebra 2 before greek.. lol

whpalmer4 · Answer

This problem is a nice one because it involves many of the tools in the toolbox, giving you a chance to see where each one is best used, except for standard form.  Standard form is convenient if you want to quickly graph a line, because it is easy to determine the x and y-intercepts from standard form, and once you know them, you plot those two points, slap down your ruler and draw a line through them.

In standard form:
Ax + By = C

x-intercept is the point where the line crosses the x-axis, so y = 0, giving us Ax = C, so the x-intercept is at (C/A, 0).  Similarly, for the y-intercept, that's the point where the line crosses the y-axis, at x = 0, so By = C, and the y-intercept is at (0, C/B).  I trust you can see how I arrived at those results?  For the first case, Ax + B(0) = C, Ax = C, x = C/A; for the second case, A(0) + By = C, By = C, y = C/B.

whpalmer4 · Answer

Point-slope form is handy when you know a point and the slope.  Slope-intercept form is handy when you know the slope and the y-intercept: if you think about it, that's just a special case of point-slope form where x0 =  0:

$$y-y_0 = m(x-x_0)$$ $$y = m(x - 0) + y_0$$$$y = mx +y_0$$But y0 is just the y-value of the y-intercept in this case, so y_0 = b, giving us our old friend y=mx+b.

whpalmer4 · Answer

Much of this isn't really difficult, it just takes the right explanation for you to understand it, and then plenty of practice to make it all second-nature.  Unfortunately, not every teacher can provide the right explanation for every student, and many students aren't willing to do the practice.

anonymous · Answer

Yes. i undersand it! u should be a teacher!!