Sure, let’s break this problem down step by step.
### Given equation:
[tex]\[ 5x - y = 6 \][/tex]
### (a) Writing the equation in slope-intercept form ([tex]\( y = mx + b \)[/tex]):
First, we need to solve for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex].
1. Start with the given equation:
[tex]\[ 5x - y = 6 \][/tex]
2. Isolate [tex]\( y \)[/tex] on one side of the equation:
[tex]\[ -y = -5x + 6 \][/tex]
3. Multiply both sides by [tex]\(-1\)[/tex] to get [tex]\( y \)[/tex] by itself:
[tex]\[ y = 5x - 6 \][/tex]
Therefore, the equation in slope-intercept form is:
[tex]\[ y = 5x - 6 \][/tex]
### (b) The slope of the line:
The slope-intercept form of the equation is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope.
From the equation [tex]\( y = 5x - 6 \)[/tex], we see that the coefficient of [tex]\( x \)[/tex] is 5. Therefore, the slope ([tex]\( m \)[/tex]) is:
[tex]\[ 5 \][/tex]
### (c) The y-intercept:
The y-intercept in the equation [tex]\( y = mx + b \)[/tex] is given by the constant term [tex]\( b \)[/tex].
From the equation [tex]\( y = 5x - 6 \)[/tex], the constant term is [tex]\(-6\)[/tex]. This means the y-intercept is the point [tex]\((0, b)\)[/tex], or:
[tex]\[ (0, -6) \][/tex]
### Summary:
(a) The equation in slope-intercept form is [tex]\( y = 5x - 6 \)[/tex].
(b) The slope is [tex]\( 5 \)[/tex].
(c) The y-intercept is [tex]\( (0, -6) \)[/tex].
