Question

Nico is trying to write an equation in slope-intercept form for a line that passes through the point (1,2) and has a slope of −1/2. What is the y-intercept of this line, rounded to the nearest tenth?

Answer 1

To write the equation of a line in slope-intercept form, which is given by \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, we can start with the given slope and point.

Given:
- The slope \( m = -\frac{1}{2} \)
- The point \( (1, 2) \)

We can substitute the point into the equation along with the slope to find the y-intercept \( b \).

1. Substitute \( x = 1 \) and \( y = 2 \) into the equation \( y = mx + b \):

\[
2 = -\frac{1}{2}(1) + b
\]

2. Simplify the equation:

\[
2 = -\frac{1}{2} + b
\]

3. To solve for \( b \), add \(\frac{1}{2}\) to both sides:

\[
2 + \frac{1}{2} = b
\]

4. Convert \( 2 \) to a fraction with a denominator of 2:

\[
\frac{4}{2} + \frac{1}{2} = b
\]

5. Combine the fractions:

\[
\frac{4 + 1}{2} = b
\]

\[
\frac{5}{2} = b
\]

6. Convert \(\frac{5}{2}\) to a decimal:

\[
\frac{5}{2} = 2.5
\]

Thus, the y-intercept \( b \) is \( 2.5 \), which is already rounded to the nearest tenth.

Therefore, the y-intercept of the line is \( \boxed{2.5} \).