Write an equation in standard form of the line that passes through the given points

(-1,2) (5,4)
I not sure about this one can someone show me how to do it?

slope = (4-2)/(5-(-1)) = 1/3

pick (5,4)
y-4 = (1/3)(x-5)
times 3
3y - 12 = x - 5
x - 3y = -7

check: does the point I didn't use satisfy the equation?
for (-1,2)
LS = -1 - 3(2)
= -7
= RS
......... all is good!

Thank You

To find the equation of a line in standard form, you can use the formula:

Ax + By = C

where A, B, and C are constants.

Step 1: Find the slope of the line

The slope (m) of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:

m = (y2 - y1) / (x2 - x1)

Using the points (-1, 2) and (5, 4), the slope would be:

m = (4 - 2) / (5 - (-1))
= 2 / 6
= 1/3

Step 2: Use the slope-intercept form to find the equation

The slope-intercept form of a line is:

y = mx + b

where m is the slope and b is the y-intercept.

Substituting the slope (1/3) and one of the given points (5, 4) into the equation, we can solve for b:

4 = (1/3)(5) + b
4 = 5/3 + b
12/3 - 5/3 = b
7/3 = b

So the equation in slope-intercept form is:

y = (1/3)x + 7/3

Step 3: Convert to standard form

To convert the equation to standard form (Ax + By = C), we multiply the entire equation by 3 to eliminate any fractions:

3y = x + 7

Then we rearrange the equation to have x and y terms on the same side:

x - 3y = -7

So, the equation of the line passing through the points (-1, 2) and (5, 4) in standard form is:

x - 3y = -7