Question
Write the linear equation in slope-intercept form. \( \begin{array}{lll}\text { 5. } 2 x+y=17 & \text { 6. } 5 x-y=\frac{1}{4} & \text { 7. }-\frac{1}{2} x+y=10\end{array} \)
Ask by Campos Young. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The slope-intercept forms of the equations are:
5. \( y = -2x + 17 \)
6. \( y = 5x - \frac{1}{4} \)
7. \( y = \frac{1}{2}x + 10 \)
Solution
We want to write each equation in the form y = mx + b, where m is the slope and b is the y-intercept.
For equation 5:
2x + y = 17
Subtract 2x from both sides:
y = 17 − 2x
Rewrite as:
y = −2x + 17
For equation 6:
5x − y = 1/4
Subtract 5x from both sides:
−y = 1/4 − 5x
Multiply both sides by −1:
y = 5x − 1/4
For equation 7:
(−1/2)x + y = 10
Add (1/2)x to both sides:
y = (1/2)x + 10
Thus, the slope-intercept forms are:
5. y = −2x + 17
6. y = 5x − 1/4
7. y = (1/2)x + 10
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To convert each of these equations into slope-intercept form, \(y = mx + b\), we'll solve for \(y\). For \(2x + y = 17\): - Subtract \(2x\) from both sides: \(y = -2x + 17\). For \(5x - y = \frac{1}{4}\): - Add \(y\) to both sides: \(y = 5x - \frac{1}{4}\). For \(-\frac{1}{2}x + y = 10\): - Add \(\frac{1}{2}x\) to both sides: \(y = \frac{1}{2}x + 10\). In slope-intercept form, we have: 1. \(y = -2x + 17\) 2. \(y = 5x - \frac{1}{4}\) 3. \(y = \frac{1}{2}x + 10\)
