Yes, \(-\frac{b}{a}\) is the formula for the x-intercept of a linear equation in the standard form \(ax + by = c\).

To find the x-intercept of the equation, you set \(y = 0\) and solve for \(x\):

1. Start with the equation \(ax + by = c\).
2. Set \(y = 0\): \(ax + b(0) = c \Rightarrow ax = c\).
3. Solve for \(x\): \(x = \frac{c}{a}\).

If the equation is in the slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept, the x-intercept can be found by setting \(y = 0\):

1. Set \(y = 0\): \(0 = mx + b \Rightarrow mx = -b\).
2. Solve for \(x\): \(x = -\frac{b}{m}\).

So, in the context of \(y = mx + b\), \(-\frac{b}{m}\) is indeed the x-intercept.

Would you like more details or have any questions?

Here are some related questions:

1. How do you find the y-intercept of a linear equation?
2. What is the standard form of a linear equation?
3. How can you convert a linear equation from standard form to slope-intercept form?
4. What is the significance of the slope in a linear equation?
5. How do you find the slope of a line given two points?
6. Can a linear equation have more than one x-intercept? Why or why not?
7. What is the relationship between the slope and the angle of the line with the x-axis?
8. How do you determine if two lines are parallel?

**Tip:** When dealing with linear equations, always remember that the coefficients and constants give you direct information about the line's slope and intercepts, making it easier to analyze and graph the equation.

Explore how to find the x-intercept of linear equations using the formula -b/a. This solution covers both standard form (ax + by = c) and slope-intercept form (y = mx + b) equations, detailing step-by-step methods to determine the x-intercept. Suitable for students in Grades 7-9.

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