Find an equation in standard form for the line that passes through the given points.

To find the equation of the line in standard form that passes through the points (0, 4) and (7, 0), follow these steps:

1. Find the slope (m):

The slope formula is ( m = frac{y_2 – y_1}{x_2 – x_1} ).

Using the points (0, 4) as (x₁, y₁) and (7, 0) as (x₂, y₂):

[

m = frac{0 – 4}{7 – 0} = frac{-4}{7}

]

2. Use point-slope form:

The point-slope form of a line is given by ( y – y_1 = m(x – x_1) ).

Using point (0, 4):

[

y – 4 = -frac{4}{7}(x – 0)

]

Simplifying:

[

y – 4 = -frac{4}{7}x

]

[

y = -frac{4}{7}x + 4

]

3. Convert to standard form (Ax + By = C):

Rearranging gives:

[

frac{4}{7}x + y = 4

]