Pregunta
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
Solución de inteligencia artificial de Upstudy
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The equation of the line is \( y = -\frac{7}{8}x + \frac{9}{7} \).
Solución
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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Simplifique esta solución 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.
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