Schmidt Brewer
02/10/2024 · Senior High School
The graph of the equation \( 2 x-3 y=7 \) is a line. Homework Help a. Find the \( x \)-and \( y \)-intercepts and graph the line using these two points. b. If a point on this line has an \( x \)-coordinate of 10 , what is its \( y \)-coordinate?
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
a. To find the \( x \)-intercept, we set \( y = 0 \) and solve for \( x \):
\[ 2x - 3(0) = 7 \]
\[ 2x = 7 \]
\[ x = \frac{7}{2} \]
So the \( x \)-intercept is \( \left(\frac{7}{2}, 0\right) \).
To find the \( y \)-intercept, we set \( x = 0 \) and solve for \( y \):
\[ 2(0) - 3y = 7 \]
\[ -3y = 7 \]
\[ y = -\frac{7}{3} \]
So the \( y \)-intercept is \( \left(0, -\frac{7}{3}\right) \).
Now we can graph the line using these two points.
b. To find the \( y \)-coordinate when \( x = 10 \), we substitute \( x = 10 \) into the equation and solve for \( y \):
\[ 2(10) - 3y = 7 \]
\[ 20 - 3y = 7 \]
\[ -3y = 7 - 20 \]
\[ -3y = -13 \]
\[ y = \frac{-13}{-3} \]
\[ y = \frac{13}{3} \]
So when \( x = 10 \), the \( y \)-coordinate is \( \frac{13}{3} \).
Quick Answer
a. The \( x \)-intercept is \( \left(\frac{7}{2}, 0\right) \) and the \( y \)-intercept is \( \left(0, -\frac{7}{3}\right) \). Graph the line using these points.
b. When \( x = 10 \), the \( y \)-coordinate is \( \frac{13}{3} \).
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