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 enarest tenth?

Answer 1

To find the equation of the line in slope-intercept form \( y = mx + b \), we can use the given slope \( m = -\frac{1}{2} \) and the point \( (1, 2) \) to solve for the y-intercept \( b \).

1. Start by substituting the slope and the coordinates of the point \( (1, 2) \) into the slope-intercept formula:

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

2. Simplify the right side:

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

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

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

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

\[ 2 = \frac{4}{2} \]

Now adding:

\[ \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \]

5. Thus, we have:

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

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

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

7. Finally, round the y-intercept to the nearest tenth:

The y-intercept \( b \) is \( 2.5 \) (already in the appropriate format).

So, the y-intercept of the line, rounded to the nearest tenth, is:

\[ \boxed{2.5} \]