To determine which of the given equations is in slope-intercept form, let's first understand what slope-intercept form is.
The slope-intercept form of a linear equation is given by:
[tex]\[ y = mx + b \][/tex]
where:
- [tex]\( m \)[/tex] represents the slope of the line.
- [tex]\( b \)[/tex] represents the y-intercept, where the line crosses the y-axis.
Now, let's examine each option to see if it fits the slope-intercept form.
Option A: [tex]\( 5y = 5x - 3 \)[/tex]
We need to solve for [tex]\( y \)[/tex] to see if it can be rewritten in slope-intercept form:
[tex]\[ 5y = 5x - 3 \][/tex]
[tex]\[ y = \frac{5x - 3}{5} \][/tex]
[tex]\[ y = x - \frac{3}{5} \][/tex]
This is now in the form [tex]\( y = mx + b \)[/tex] with [tex]\( m = 1 \)[/tex] and [tex]\( b = -\frac{3}{5} \)[/tex]. So, Option A can be rewritten in slope-intercept form.
Option B: [tex]\( y = 8x + 5 \)[/tex]
This equation is already in the slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m = 8 \)[/tex] and [tex]\( b = 5 \)[/tex].
Option C: [tex]\( 6x + y = 7 \)[/tex]
We need to solve for [tex]\( y \)[/tex]:
[tex]\[ y = 7 - 6x \][/tex]
[tex]\[ y = -6x + 7 \][/tex]
This is now in the slope-intercept form [tex]\( y = mx + b \)[/tex] with [tex]\( m = -6 \)[/tex] and [tex]\( b = 7 \)[/tex]. So, Option C can be rewritten in slope-intercept form.
Option D: [tex]\( y - 9 = 5(x - 2) \)[/tex]
First, we can simplify this into slope-intercept form:
[tex]\[ y - 9 = 5x - 10 \][/tex]
[tex]\[ y = 5x - 1 \][/tex]
This is now in the slope-intercept form [tex]\( y = mx + b \)[/tex] with [tex]\( m = 5 \)[/tex] and [tex]\( b = -1 \)[/tex]. So, Option D can also be rewritten in slope-intercept form.
Conclusion:
Among the given options, Option B: [tex]\( y = 8x + 5 \)[/tex] is the equation that is already in the slope-intercept form without needing any manipulation. Thus, the correct answer is:
B. [tex]\( y = 8x + 5 \)[/tex]
