Question
With slope \( -\frac{7}{8} \), through \( \left(0, \frac{9}{7}\right) \) The equation of the line is \( y=\square \). (Simplify your answer. Use integers or fractions for any numbers in the expressio
Ask by Martin Weston. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The equation of the line is \( y = -\frac{7}{8}x + \frac{9}{7} \).
Solution
1. The slope-intercept form of a line is given by:
\[
y = mx + b
\]
where \( m \) is the slope and \( b \) is the \( y \)-intercept.
2. Given the slope \( m = -\frac{7}{8} \) and the point \(\left(0, \frac{9}{7}\right)\), note that the \( y \)-coordinate of this point is the \( y \)-intercept. Hence, \( b = \frac{9}{7} \).
3. Substitute the values into the slope-intercept form:
\[
y = -\frac{7}{8}x + \frac{9}{7}
\]
4. Therefore, the equation of the line is:
\[
y = -\frac{7}{8}x + \frac{9}{7}
\]
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Simplify this solution Bonus Knowledge
To write the equation of the line in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, we have the slope \( m = -\frac{7}{8} \) and the y-intercept \( b = \frac{9}{7} \). Plugging these values into the formula, we get: \[ y = -\frac{7}{8}x + \frac{9}{7} \] This is the equation of the line! For further simplification, you can find a common denominator to combine terms if needed, but this equation is perfectly valid as it stands. Just remember to visualize that slope descending, which corresponds to our negative slope.
