Consider the line y=-3x+3.

Mathematics

1 answer:

emmainna [20.7K]2 years ago

7 0

Answer:

$y= 3x+17; y= -\frac13x +\frac{11}3$

Step-by-step explanation:

First problem. If you want a parallel to a given line, you keep the slope.

Then we use the point-slope form of a line

$y-y_0=m(x-x_0)$ and we plug in there everything we need.

$y-5=3(x+4) \rightarrow y=3x+12+5\\y=3x+17$

The second is quite similar. This time we want the perpendicular. It means that the product of the slopes has to be -1.

$3\cdot m = -1 \rightarrow m=-\frac13$

At this point we have everything, let's replace and write down the line in a better looking form

$y-5=-\frac13(x+4) \rightarrow y= -\frac13 x -\frac43 +5\\y= -\frac13x -\frac43 +\frac{15}3 \rightarrow y= -\frac13x +\frac{11}3$

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A cube has a length, width and height of 6 feet. What is the volume in cubic INCHES?

rodikova [14]

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3 years ago

3y-6=3x and y+2x=5 solve the system of linear equations by graphing PLEASE SHOW WORK

Dmitry_Shevchenko [17]

Answer:

(x, y) = (1, 3)

Step-by-step explanation:

The "work" of solving by graphing is typing the equations into a graphing calculator and highlighting the point of intersection.

___

If you're graphing these by hand, there are a couple of strategies you can use. One is to make use of the intercepts of the line. For each of these, you need to rearrange the equation to a suitable form.

3y -6 = 3x

To put this into "intercept form", put the variable terms on one side of the equal sign and the constant on the other. Then divide by the constant and express the resulting variable coefficients as denominators.

3x -3y = -6

x/(-6/3) +y/(-6/-3) = 1

x/(-2) + y/2 = 1 . . . . . . The x-intercept is -2; the y-intercept is 2.

Plot the intercept points and draw a line through them.

y +2x = 5

The intercepts for this one are found by dividing by 5:

x/(5/2) + y/5 = 1 . . . . . . The x-intercept is 2.5; the y-intercept is 5.

The other strategy you can use for this one is to rearrange the equation to slope-intercept form and make use of those numbers.

y = -2x + 5

The y-intercept is 5 (as we already found above), and the slope is -2. That means the line drops 2 units for each unit it goes to the right. Apart from the y-intercept, other points on this line will be (1, 3), (2, 1), (3, -1).

Solution

When you plot these lines, you find they intersect at (1, 3). That is the solution to the system of equations, the values of x and y that satisfy both equations.