How can I write an equation of the linefor example (2,-7) 8x +3y=2. I keep mnissing the most important step. Some of these I have done quite well, like x+6y=9. Please help with the detail because I do remember when to divide.

Equation of a line requires either:

a. two points
b. one point, and a slope

What exactly are you trying to do?

I am trying to wite the equation in the form

y=mx+b

The equation has two given point (3,-8), then an equation Example (3,-8) 8x +3y=6(just an example)

For example (8,5) 8x+3y=7
y-y=m(x-x)
y-5=m(x-x)
y-5=3/8(x-)
=3/8x-8

To write an equation of a line, you need to use the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.

To find the equation of a line given a specific point and a different form of the equation, such as standard form (Ax + By = C), you need to follow these steps:

Step 1: Convert the equation to slope-intercept form:

For example, let's convert the equation 8x + 3y = 2 to slope-intercept form.

8x + 3y = 2

Start by isolating y on one side of the equation.

3y = -8x + 2

Divide both sides of the equation by 3 to solve for y:

y = (-8/3)x + 2/3

Now the equation is in the form y = mx + b, where m is the slope and b is the y-intercept.

Step 2: Plug in the given point coordinates into the equation.

For example, let's use the point (2, -7) and the equation y = (-8/3)x + 2/3.

Substitute x = 2 and y = -7 into the equation:

-7 = (-8/3)(2) + 2/3

Simplify the equation:

-7 = -16/3 + 2/3

Step 3: Solve for the missing variable.

To solve for the missing variable, combine the fractions on the right side of the equation:

-7 = (-16 + 2)/3

-7 = -14/3

Finally, multiply both sides of the equation by 3 to eliminate the fraction:

3*(-7) = -14

-21 = -14

So, the equation is inconsistent, meaning there is no solution for that given point in the equation 8x + 3y = 2.

In the second example you provided, x + 6y = 9, the equation is already in standard form. To convert it to slope-intercept form, you can follow the same steps:

x + 6y = 9

Start by isolating y:

6y = -x + 9

Divide both sides by 6:

y = -(1/6)x + 9/6

Simplify the fraction:

y = -(1/6)x + 3/2

Now the equation is in the form y = mx + b, where m is the slope and b is the y-intercept.