Rewrite the following equation in slope-intercept form.



4*x* − 19*y* = 1


To rewrite the equation \( 4x - 19y = 1 \) in slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, follow these steps:

1. Start with the original equation:
   \[
   4x - 19y = 1
   \]

2. Isolate \( y \) on one side. First, subtract \( 4x \) from both sides:
   \[
   -19y = -4x + 1
   \]

3. Now, divide every term by \( -19 \) to solve for \( y \):
   \[
   y = \frac{4}{19}x - \frac{1}{19}
   \]

So, the slope-intercept form of the equation is:
\[
y = \frac{4}{19}x - \frac{1}{19}
\]

Would you like further clarification or more details on this?

Here are 5 related questions for further exploration:

1. What is the slope of the line in the given equation?
2. What is the y-intercept of the line in this equation?
3. How do you find the x-intercept from the slope-intercept form?
4. How would you graph this line using the slope and y-intercept?
5. How can you convert a slope-intercept equation back into standard form?

**Tip:** When rewriting in slope-intercept form, always aim to isolate \( y \) on one side.

Rewrite the following equation in slope-intercept form: 4x − 19y = 1

Learn how to rewrite the linear equation 4x − 19y = 1 in slope-intercept form. This step-by-step solution explains key algebraic concepts like isolating y and identifying the slope and y-intercept. Ideal for students in Grades 8-10.

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