Write an equation in standard form for the line that passes through the given points. (0,4) and (7,0) The equation of the line in standard form is ____. (Type your answer in standard form.)
Find an equation in standard form for the line that passes through the given points.
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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
]