Which of the following linear equation can passes through the point(3,-2) a. x+y=0 b. 2x+3y=0 c. x+y=5 d. 2x-y=0
Answers
Answer:
hehe
Step-by-step explanation:
3x + 4y = - 8
The equation of a line in standard form is Ax + By = C
where A is a positive integer and B, C are integers
Express the line in ' slope- intercept form '
y = mx + c → (m is the slope and c is the y-intercept)
here m = - and c = - 2
hence y = - x - 2 → equation in slope- intercept form
multiply all terms by 4
4y = - 3x - 8
add 3x to both sides
3x + 4y = - 8 → in standard form
Step-by-step explanation:
Yes, you can!
First, there is an easy way to determine if two lines are parallel to each other just by looking at their respective linear equations (once they are in slope-intercept form)
The equation above, 2x+3y+4 =0, is technically in standard form. The standard formula for a linear equation in standard form is ax + by = c. In the equation above, the “c” value was added to the left side so that the right side was equal to zero. So the equation in “true” standard form would be 2x + 3y = -4.
Although standard form can be useful in some scenarios, we will have to convert this equation into slope-intercept form for us to work with it.
The equation for slope-intercept form is:
y=mx+b
The meaning of these values is explained at the bottom*.
So, this just means that we have to solve for Y.
2x + 3y + 4 = 0 | Here is our original equation.
I am now going to isolate the Y variable on one side, by subtracting 3y from both sides of the equation.
2x + 3y + 4 = 0
turns into
2x + 4 = -3y.
Now, I am going to divide both sides of the equation by -3, because the y value has a coefficient of -3. This means that y is being multiplied by -3, but we need to get y all by itself in order to put the equation into slope-intercept form.
2x + 4 = -3y
turns into
y=−23x+−43
Now, compare this to the original slope-intercept formula, Y = mx + b.
In this case, our m value is −23 . This represents the slope. If two lines have the same slope, then they are parallel. You can find more about that by watching this video here: Proof: parallel lines have the same slope
All we know at this point is the slope for our first equation. How can we determine the slope of an entire line using only two points?
Well, there are many ways to do this. But the simplest way would to be to use the slope formula. The slope formula calculates the slope of a line using the x and y values from two different points on a line. The formula is:
riserun=y2−y1x2−x1
Since slope is just rise over run, we will plug in the values of the points (9,4) and (3,8) into the formula to find our slope. If the value of our slope is equal to −23 , then we know that the two lines are parallel. If the slopes are not equal to one another, then the two lines are not parallel.
First, let’s plug in the corresponding x and y values:
y2−y1x2−x1=8−43−9
Now, let’s simplify the fraction:
8−43−9=4−6=−46=−23
So the slope of our second line is also −23 . Because the slopes of both lines are −23 , this tells us that the lines are parallel.
You could also find the slope of the two points (9,4) and (3,8) using point-slope form, but I won’t get into that now.
And just for kicks…
Another outcome could be that the lines have the exact same equation (that is, to say, both lines are actually the same line, because the points (9,4) and (3,8) actually fall on the graph of 2x + 3y + 4 = 0. To quickly test this, we can plug in the x-value for the first point, 9, into the equation 2x + 3y + 4 = 0 to see if y = 4 for this value of x.
2(9)+3y+4=0
then, we solve for Y.
18+3y+4=0
22+3y=0
3y=−22
y=−223
Okay, so because we know that the first line 2x + 3y + 4 has the point (9, -22/3) and the second line has the point (9, 4), this tells us that the two lines, are, in fact, not the same line, and we can now say without a doubt th