Let's start with the given equation:
[tex]\[ 2x + 3y = 1470 \][/tex]
Our goal is to convert this equation into the slope-intercept form, which is:
[tex]\[ y = mx + b \][/tex]
where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
1. Isolate the [tex]\( y \)[/tex]-term on one side of the equation:
[tex]\[ 3y = 1470 - 2x \][/tex]
2. Solve for [tex]\( y \)[/tex] by dividing every term by 3:
[tex]\[ y = \frac{1470}{3} - \frac{2x}{3} \][/tex]
3. Simplify the constants:
[tex]\[ y = 490 - \frac{2}{3}x \][/tex]
Rearrange the terms to match the slope-intercept form:
[tex]\[ y = -\frac{2}{3}x + 490 \][/tex]
Now, identify the slope and y-intercept.
- The slope ([tex]\( m \)[/tex]) is the coefficient of [tex]\( x \)[/tex], which is [tex]\( -\frac{2}{3} \)[/tex].
- The y-intercept ([tex]\( b \)[/tex]) is the constant term, which is [tex]\( 490 \)[/tex].
Therefore, the slope is [tex]\( -0.67 \)[/tex] (rounded to two decimal places) and the y-intercept is [tex]\( 490 \)[/tex].
