Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Get quick and reliable solutions to your questions from a community of seasoned experts on our user-friendly platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
To find the [tex]$y$[/tex]-coordinate of the [tex]$y$[/tex]-intercept of line [tex]\( p \)[/tex], we need to use the slope-intercept form of a linear equation, which is given by:
[tex]\[ y = mx + b \][/tex]
Here, [tex]\( m \)[/tex] represents the slope, and [tex]\( b \)[/tex] represents the [tex]$y$[/tex]-intercept.
Given:
- The slope [tex]\( m \)[/tex] of line [tex]\( p \)[/tex] is [tex]\( -\frac{5}{3} \)[/tex].
- The [tex]$x$[/tex]-intercept of the line is at the point [tex]\((-6, 0)\)[/tex].
The [tex]$x$[/tex]-intercept is a point where the line crosses the [tex]$x$[/tex]-axis, meaning the [tex]$y$[/tex]-coordinate at that point is [tex]\( 0 \)[/tex]. We can use this point to find the [tex]$y$[/tex]-intercept by plugging it into the slope-intercept equation:
[tex]\[ y = mx + b \][/tex]
Given the point [tex]\((-6, 0)\)[/tex], we substitute [tex]\( x = -6 \)[/tex] and [tex]\( y = 0 \)[/tex] into the equation:
[tex]\[ 0 = \left( -\frac{5}{3} \right) (-6) + b \][/tex]
First, calculate the product of the slope and the [tex]\( x \)[/tex]-coordinate:
[tex]\[ \left( -\frac{5}{3} \right) (-6) = \frac{5}{3} \times 6 = \frac{30}{3} = 10 \][/tex]
Now our equation looks like:
[tex]\[ 0 = 10 + b \][/tex]
To find [tex]\( b \)[/tex], subtract [tex]\( 10 \)[/tex] from both sides:
[tex]\[ b = 0 - 10 \][/tex]
[tex]\[ b = -10 \][/tex]
So, the [tex]$y$[/tex]-coordinate of the [tex]$y$[/tex]-intercept of line [tex]\( p \)[/tex] is:
[tex]\[ \boxed{-10} \][/tex]
[tex]\[ y = mx + b \][/tex]
Here, [tex]\( m \)[/tex] represents the slope, and [tex]\( b \)[/tex] represents the [tex]$y$[/tex]-intercept.
Given:
- The slope [tex]\( m \)[/tex] of line [tex]\( p \)[/tex] is [tex]\( -\frac{5}{3} \)[/tex].
- The [tex]$x$[/tex]-intercept of the line is at the point [tex]\((-6, 0)\)[/tex].
The [tex]$x$[/tex]-intercept is a point where the line crosses the [tex]$x$[/tex]-axis, meaning the [tex]$y$[/tex]-coordinate at that point is [tex]\( 0 \)[/tex]. We can use this point to find the [tex]$y$[/tex]-intercept by plugging it into the slope-intercept equation:
[tex]\[ y = mx + b \][/tex]
Given the point [tex]\((-6, 0)\)[/tex], we substitute [tex]\( x = -6 \)[/tex] and [tex]\( y = 0 \)[/tex] into the equation:
[tex]\[ 0 = \left( -\frac{5}{3} \right) (-6) + b \][/tex]
First, calculate the product of the slope and the [tex]\( x \)[/tex]-coordinate:
[tex]\[ \left( -\frac{5}{3} \right) (-6) = \frac{5}{3} \times 6 = \frac{30}{3} = 10 \][/tex]
Now our equation looks like:
[tex]\[ 0 = 10 + b \][/tex]
To find [tex]\( b \)[/tex], subtract [tex]\( 10 \)[/tex] from both sides:
[tex]\[ b = 0 - 10 \][/tex]
[tex]\[ b = -10 \][/tex]
So, the [tex]$y$[/tex]-coordinate of the [tex]$y$[/tex]-intercept of line [tex]\( p \)[/tex] is:
[tex]\[ \boxed{-10} \][/tex]
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.