find the b with the points (1,1) and m=-1/3




To find the y-intercept \( b \) of a line, we use the slope-intercept form of a line:

\[
y = mx + b
\]

Here:
- \( m = -\frac{1}{3} \) is the slope,
- The point \( (1,1) \) means when \( x = 1 \), \( y = 1 \).

Now, substitute the values into the equation:

\[
1 = -\frac{1}{3}(1) + b
\]

Simplify:

\[
1 = -\frac{1}{3} + b
\]

To solve for \( b \), add \( \frac{1}{3} \) to both sides:

\[
1 + \frac{1}{3} = b
\]

Converting 1 to a fraction:

\[
\frac{3}{3} + \frac{1}{3} = b
\]

\[
b = \frac{4}{3}
\]

So, the y-intercept is \( b = \frac{4}{3} \).

Would you like more details or explanations?

Here are five related questions:
1. How do you graph a line using a point and the slope?
2. What is the slope-intercept form of a line?
3. How do you convert fractions to decimals when solving equations?
4. What does the slope \( m \) represent in real-world problems?
5. Can the y-intercept ever be a negative value?

**Tip:** Always substitute values carefully to avoid sign errors when solving for constants like \( b \).

find the b with the points (1,1) and m=-1/3

Learn how to find the y-intercept (b) of a line using the slope-intercept form with the point (1,1) and a slope of -1/3. This solution covers key algebra concepts and provides step-by-step calculations suitable for students in Grades 8-10.

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