Question

A) 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? (1 point)

Answer 1

To write the equation of a line in slope-intercept form (which is \(y = mx + b\)), we need to know the slope (\(m\)) and the y-intercept (\(b\)). We are given that the slope \(m = -\frac{1}{2}\) and the line passes through the point (1, 2).

1. Substitute the known values into the slope-intercept equation:
\[
2 = -\frac{1}{2}(1) + b
\]

2. Simplify this equation:
\[
2 = -\frac{1}{2} + b
\]

3. To isolate \(b\), add \(\frac{1}{2}\) to both sides of the equation:
\[
b = 2 + \frac{1}{2}
\]

4. Convert \(2\) to a fraction for easier addition:
\[
2 = \frac{4}{2}
\]
So,
\[
b = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}
\]

5. Now, convert \(\frac{5}{2}\) to a decimal:
\[
\frac{5}{2} = 2.5
\]

Therefore, the y-intercept \(b\) is \(2.5\).

So, the y-intercept of the line, rounded to the nearest tenth, is **2.5**.