Write the equation, 7x+4y=−7, in slope-intercept form.



To write the equation \(7x + 4y = -7\) in slope-intercept form, which is \(y = mx + b\), follow these steps:

1. Start with the given equation:
   \[
   7x + 4y = -7
   \]

2. Isolate the \(y\)-term on one side by subtracting \(7x\) from both sides:
   \[
   4y = -7x - 7
   \]

3. Now, divide both sides of the equation by \(4\) to solve for \(y\):
   \[
   y = \frac{-7x - 7}{4}
   \]

4. Simplify the right side:
   \[
   y = -\frac{7}{4}x - \frac{7}{4}
   \]

Now, the equation is in slope-intercept form:
\[
y = -\frac{7}{4}x - \frac{7}{4}
\]

Here, the slope \(m = -\frac{7}{4}\) and the y-intercept \(b = -\frac{7}{4}\).

Would you like more details on how this form relates to graphing? 

Here are 5 related questions:
1. What does the slope represent in this equation?
2. How can you determine the y-intercept from the equation?
3. How would you find the x-intercept from this equation?
4. How can the equation be rewritten in standard form?
5. How does changing the slope affect the graph of the line?

**Tip:** The slope indicates how steep the line is and whether it rises or falls as \(x\) increases.

Write the equation, 7x+4y=−7, in slope-intercept form.

Learn how to convert the linear equation 7x + 4y = -7 to slope-intercept form (y = mx + b) with a step-by-step guide. This solution involves isolating the y-term and dividing to find the slope (m) and y-intercept (b). Suitable for students in Grades 8-10.

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