To convert the given equation into slope-intercept form, which is [tex]\( y = mx + b \)[/tex], we follow these steps:
1. Start with the given equation:
[tex]\[
2x + 5y = 2
\][/tex]
2. Isolate the [tex]\( y \)[/tex] term on one side. To do this, subtract [tex]\( 2x \)[/tex] from both sides:
[tex]\[
5y = -2x + 2
\][/tex]
3. Solve for [tex]\( y \)[/tex] by dividing every term by 5:
[tex]\[
y = \frac{-2x + 2}{5}
\][/tex]
4. Simplify the equation:
[tex]\[
y = \left( \frac{-2}{5} \right) x + \frac{2}{5}
\][/tex]
Thus, the equation in slope-intercept form is:
[tex]\[
y = -\frac{2}{5}x + \frac{2}{5}
\][/tex]
From this equation, we can identify the slope [tex]\( m \)[/tex] and the y-intercept [tex]\( b \)[/tex]:
- The slope [tex]\( m \)[/tex] is [tex]\( -\frac{2}{5} \)[/tex] or [tex]\(-0.4\)[/tex].
- The y-intercept [tex]\( b \)[/tex] is [tex]\( \frac{2}{5} \)[/tex] or [tex]\( 0.4 \)[/tex].
So, the equation in slope-intercept form is:
[tex]\[
y = -0.4x + 0.4
\][/tex]
Remember to simplify your answer where needed, using fractions or decimals.
