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 they y-intercept of this line rounded to the nearest tenth

1 answer

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

  • The slope \( m = -\frac{1}{2} \)
  • The line passes through the point \( (1, 2) \)

We can substitute the given point \((x, y) = (1, 2)\) and the slope into the equation to find \( b \) (the y-intercept):

\[ y = mx + b \] Plugging in the values:

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

Now, simplify:

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

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

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

Converting 2 to a fraction gives us:

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

Now, converting \(\frac{5}{2}\) to a decimal gives us:

\[ b = 2.5 \]

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