Question

A coordinate plane with a line passing through the points (0, negative 4) and (2, 2). What is the equation of the graphed line written in standard form?

Answer 1

The equation of the line passing through the points (0, -4) and (2, 2) can be written in standard form as 3x - y = 4 or -3x + y = -4 after finding the slope and using point-slope form to derive the equation.

Step-by-step explanation:

To find the equation of a line in standard form, given two points, we first need to calculate the slope of the line. The slope is found by taking the difference in the y-coordinates and dividing it by the difference in the x-coordinates.

The two points provided are (0, -4) and (2, 2). Thus, the slope (m) is (2 - (-4))/(2 - 0) = 6/2 = 3. With the slope, we can use the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is one of the given points and m is the slope. Using point (0, -4), the equation becomes y - (-4) = 3(x - 0), which simplifies to y + 4 = 3x.

To write this in standard form, which is Ax + By = C, we rearrange terms to get the x and y on the same side: 3x - y = 4, which can also be written as -3x + y = -4 to have positive coefficients.

Answer 2

3x - y = 4

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

First find the equation in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (0, - 4) and (x₂, y₂ ) = (2, 2)

m =
`(2+4)/(2-0)` =
`(6)/(2)` = 3

Note the line crosses the y- axis at (0, - 4) ⇒ c = - 4

y = 3x - 4 ← in slope- intercept form

Add 4 to both sides

y + 4 = 3x ( subtract y from both sides )

4 = 3x - y, that is

3x - y = 4 ← in standard form