Pregunta
Find an equation of the line described. Write the equation in slope-intercept form. With slope \( -\frac{7}{8} \), through \( \left(0, \frac{9}{7}\right) \) The equation of the line is \( y= \). (Simplify your answer. Use integers or fractions for any numbers in the expression.)
Ask by Nichols Delgado. in the United States
Mar 11,2025
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The equation of the line is \( y = -\frac{7}{8}x + \frac{9}{7} \).
Solución
We are given the slope \( m = -\frac{7}{8} \) and a point \(\left(0, \frac{9}{7}\right)\) that lies on the line.
Since the point is \(\left(0, \frac{9}{7}\right)\), the \(y\)-intercept is \(\frac{9}{7}\). In general, a line in slope-intercept form is given by:
\[
y = mx + b
\]
Substituting in the known values:
\[
y = -\frac{7}{8}x + \frac{9}{7}
\]
Therefore, the equation of the line is:
\[
y = -\frac{7}{8}x + \frac{9}{7}
\]
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Simplifique esta solución Extra Insights
To write the equation of the line in slope-intercept form, which is \( y = mx + b \), we can use the provided slope \( -\frac{7}{8} \) and the y-intercept \( \frac{9}{7} \) (since the line passes through the point \( (0, \frac{9}{7}) \)). Thus, we can substitute these values into our equation: \[ y = -\frac{7}{8}x + \frac{9}{7} \] This is the equation of the line in slope-intercept form. Now, if you want to simplify this or convert it into a different form, remember that keeping it in slope-intercept form is often the most helpful for quickly identifying slope and y-intercept.
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