To determine which line represents the linear equation [tex]\( -3y = 15 - 4x \)[/tex], we first need to rewrite the equation in 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. Start with the original equation:
[tex]\[ -3y = 15 - 4x \][/tex]
2. Rearrange the equation to solve for [tex]\( y \)[/tex]. First, isolate [tex]\( y \)[/tex] by dividing every term by -3:
[tex]\[ y = \frac{-4x + 15}{-3} \][/tex]
Simplify the right-hand side:
[tex]\[ y = \frac{4}{3}x - 5 \][/tex]
So, the equation in slope-intercept form is:
[tex]\[ y = \frac{4}{3}x - 5 \][/tex]
3. From the slope-intercept form [tex]\( y = \frac{4}{3}x - 5 \)[/tex], we can identify the slope [tex]\( m \)[/tex] and the y-intercept [tex]\( b \)[/tex]:
- The slope [tex]\( m \)[/tex] is [tex]\(\frac{4}{3} \)[/tex]
- The y-intercept [tex]\( b \)[/tex] is [tex]\(-5\)[/tex]
Hence, the equation [tex]\( -3y = 15 - 4x \)[/tex] rewritten in slope-intercept form is [tex]\( y = \frac{4}{3}x - 5 \)[/tex]. The [tex]\( y \)[/tex]-intercept is [tex]\(-5\)[/tex], and the slope of the line is [tex]\( \frac{4}{3} \)[/tex].
To determine which line represents this equation, we need a line that has the slope [tex]\( \frac{4}{3} \)[/tex] and y-intercept [tex]\(-5\)[/tex]. This will typically be given in a graphical or multiple-choice format, so without specific options, we identify the line with these properties.
