Question
Write an equation in standard form for the line that passes through the given points. \( (0,4) \) and \( (5,0) \) The equation of the line in standard form is (Type your answer in standard form.)
Ask by Tyler Munoz. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The equation of the line in standard form is \( 4x + 5y = 20 \).
Solution
\( m = \frac{0 - 4}{5 - 0} = -\frac{4}{5} \)
The point-slope form using the point \( (0,4) \) is:
\[
y - 4 = -\frac{4}{5}(x - 0)
\]
Simplify to the slope-intercept form:
\[
y = -\frac{4}{5}x + 4
\]
To convert to standard form, multiply every term by 5:
\[
5y = -4x + 20
\]
Rearrange to obtain:
\[
4x + 5y = 20
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution The Deep Dive
To find the equation of the line in standard form using the given points \((0,4)\) and \((5,0)\), we first identify the slope \(m\). The slope formula is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 4}{5 - 0} = \frac{-4}{5} \] Using the slope-intercept form \(y = mx + b\) where \(b\) is the y-intercept (which is 4 from point \((0,4)\)), we can write the equation as: \[ y = -\frac{4}{5}x + 4 \] Now to convert this to standard form \(Ax + By = C\): 1. Multiply the entire equation by 5 to eliminate the fraction: \[ 5y = -4x + 20 \] 2. Rearranging gives: \[ 4x + 5y = 20 \] So the equation of the line in standard form is: \[ 4x + 5y = 20 \]
