Algebra help?

Question

i need help with solve 3x+4y=-24 write the equationof the line through (3,-1) and (-1,3) there 2 seperate problems

Answer 1

In the first, subtract 3x from both sides then divide both sides by 4 to get y = -3/4 x - 6, so slope = -3/4 and y-int. = -6

In the second, find the slope using y2 - y1 over x2 - x1

(3 - -1)/(-1 - 3) = 4/-4 = -1

The eqn of a line knowing a point (a,b) and the slope m is

y-b = m(x-a) so pick either point and plug in

Answer 2

3x + 4y = -24 doesn't have one particular solution, it has infinitely many. From the form of the equation we know that it is a straight line, so put in a couple of values to get points on the line and you can graph it. For instance, if x = 0 we have 4y = -24 so y = -6, and for y = 0 we have 3x = -24 so x = -8. So two points on the line are (0, -6) and (-8, 0).

To write the equation of the line passing through (3, -1) and (-1, 3), find the gradient: m = (y2 - y1) / (x2 - x1) = (3 - (-1)) / (-1 - 3) = 4 / (-4) = -1. Then we have y = mx + b = -x + b. Substituting in a known point, say (3, -1), gives -1 = -3 + b and thus b = 2. (You can check that if we use the other point we get the same answer.) So the line is y = -x + 2 or y = 2 - x or x + y = 2 (all these are equivalent).

Answer 3

Put the equation in the proper linear form with y on the LHS:
4y = -3x - 24
y = -3x/4 - 24/4 = -(3/4)x - 6

In slope intercept form, y = mx + b where m is the slope and b is where the line crosses the y axis; so
y(x=3) = 3m + b = -1
y(x=-1)= -m + b = 3 and subtract the second from the first:

4m = -4 or m = -1, so you know the slope and put it into the first equation y = (-1)x + b or y(x=3) = -1(3) + b = -1
or b = -1 + 3 = 2 and the equation is y = -x + 2 ; but to be sure test it with the second equation:
y(x=-1) = -(-1) + 2 = 1 + 2 = 3 as required

Answer 4

The first problem cannot be solved, as there is just one equation with two unknowns. Are you sure you have typed it correctly?

The second can be done as follows:

Find the gradient, m = (y1-y2)/(x1-x2) = (-1-3)/(3--1) = -4/4 = -1

then the equation is given by: y - y1 = m (x - x1)

So y - -1 = -1(x - 3)

So y + 1 = 3 - x

So y = 2 - x

And that is the equation of the line.

Answer 5

Jessica, the first question probably is looking for you to solve in terms of y. This means you use addition-subtraction-multiplication-division properties to isolate y on one side of the equal sign.

The second question requires you to solve for slope (y2-y1)/(x2-x1) and then plug your slope and one of the points into the following equation (called point-slope formula):

y-y1 = m(x-x1) where m = slope. Again, you probably need to solve in terms of y (called slope-intercept form)

Hope that helps!

PS: There are several solutions for the first equation, so I am sure this is not what your teacher is looking for....

Answer 6

x=-4
y=-3