when writing linear equations, how do you determine which form of a line to use? choose 1 set of points from the choices below. then, solve the problem and post your solution, showing your steps. write an equation in point-slope form for the line that passes through one of the following pairs of points (you may choose the pair you want to work with). then, use the same set of points to write the equation in standard form and again in slope-intercept form. point pairs (5,1),(-3,4),(0,-2),(3,2),(-2,-1),(1,2)

Please help ! I'm am so lost In this one

I don't blame you for being lost, since the question is poorly worded.

Since they started off my talking about linear equations, I had assumed that all the given points lie on the same straight line. But they do not.

anyway...

suppose we take the first two points (5,1) and (-3,4)
I assume you know how to find slope
slope = (4-1)/(-3-5) = 3/-8 = - 3/8

Using point-slope form, I will use (5,1)
y - 1 = (-3/8)(x-5)
times 8
8y - 8 = -3x + 15
3x + 8y = -23 or 3x + 8y + 23 = 0

I haven't taught math in over 17 years but I recall the following

3x + 8y = -23 ------ standard form
3x + 8y + 23 = 0 --- general form

once you have one of these, in two steps I can change them to slope y-intercept form
3x + 8y = -23
8y = -3x - 23
y = (-3/8)x - 23/8

There is also a form simply called the intecept form

start with the standard form
3x + 8y = -23
divide each term by the constant on the right side
3x/-23 + 8y/-23 = 1
x/(-23/3) + y/(-23/8) = 1
the constant below x is the x-intercept
the constant below y is the y-intercept

To determine which form of a line to use when writing linear equations, you need to consider the given information or the specific problem requirements. There are three common forms of linear equations: point-slope form, standard form, and slope-intercept form.

1. Point-Slope Form:
Point-slope form is typically used when you are given a point on the line and the slope of the line.
The general equation of a line in point-slope form is: y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.

2. Standard Form:
Standard form is usually used when you want to write the equation in a more simplified or standardized form.
The general equation of a line in standard form is: Ax + By = C, where A, B, and C are constants, and A and B are not both zero.

3. Slope-Intercept Form:
Slope-intercept form is commonly used when you know the slope of the line and the y-intercept.
The general equation of a line in slope-intercept form is: y = mx + b, where m is the slope and b is the y-intercept.

Now, let's choose one set of points from the given options and work on writing the equation in each form.

Let's choose the point pair (3, 2).
1. Point-Slope Form:
We need the slope of the line to use this form. However, the slope is not given in the problem. Therefore, we need to calculate it using the provided points. The slope (m) between two points (x₁, y₁) and (x₂, y₂) can be calculated using the formula: m = (y₂ - y₁) / (x₂ - x₁).

Let's calculate the slope using the points (5, 1) and (3, 2):
m = (2 - 1) / (3 - 5) = 1 / (-2) = -1/2

Now we can use the point-slope form with the point (3, 2) and the slope (-1/2):
y - 2 = -1/2(x - 3)

2. Standard Form:
To convert the equation to standard form, we need to eliminate the fraction by multiplying through by 2:
2(y - 2) = -1(x - 3)
2y - 4 = -x + 3
x + 2y = 7

3. Slope-Intercept Form:
To convert the equation to slope-intercept form, we need to solve for y:
y - 2 = -1/2(x - 3)
y - 2 = -1/2x + 3/2
y = -1/2x + 3/2 + 2
y = -1/2x + 3/2 + 4/2
y = -1/2x + 7/2

So, the equation for the line passing through the points (3, 2) in each form is:
- Point-Slope Form: y - 2 = -1/2(x - 3)
- Standard Form: x + 2y = 7
- Slope-Intercept Form: y = -1/2x + 7/2