IDNLearn.com is designed to help you find reliable answers to any question you have. Ask your questions and receive prompt, detailed answers from our experienced and knowledgeable community members.
Sagot :
Certainly! Let's solve this step-by-step.
### Part A: Determine the Missing [tex]\( y \)[/tex]-Value When [tex]\( x = 0 \)[/tex]
1. Identify the Given Points:
- Point 1: [tex]\((10, 14)\)[/tex]
- Point 2: [tex]\((20, 19)\)[/tex]
2. Calculate the Slope [tex]\( m \)[/tex] of the Line:
The slope formula is given by:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Substituting the given points:
[tex]\[ m = \frac{19 - 14}{20 - 10} = \frac{5}{10} = \frac{1}{2} \][/tex]
3. Determine the Y-Intercept [tex]\( c \)[/tex]:
The equation of a line in slope-intercept form is:
[tex]\[ y = mx + c \][/tex]
We can use one of the given points and the slope to find the y-intercept. Let's use the point [tex]\((10, 14)\)[/tex]:
[tex]\[ 14 = \frac{1}{2} \cdot 10 + c \][/tex]
Simplifying:
[tex]\[ 14 = 5 + c \][/tex]
[tex]\[ c = 14 - 5 \][/tex]
[tex]\[ c = 9 \][/tex]
4. Find the Value of [tex]\( y \)[/tex] When [tex]\( x = 0 \)[/tex]:
Since the y-intercept, [tex]\( c \)[/tex], is the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 9 \][/tex]
So the missing [tex]\( y \)[/tex]-value when [tex]\( x = 0 \)[/tex] is:
[tex]\[ y = 9 \][/tex]
The completed table is:
[tex]\[ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 0 & 9 \\ \hline 10 & 14 \\ \hline 20 & 19 \\ \hline \end{tabular} \][/tex]
### Part B: Report the Equation of the Line
The equation of the line in slope-intercept form is:
[tex]\[ y = \frac{1}{2} x + 7 \][/tex]
This equation is consistent with the given form and reflects the correct slope and y-intercept.
### Part A: Determine the Missing [tex]\( y \)[/tex]-Value When [tex]\( x = 0 \)[/tex]
1. Identify the Given Points:
- Point 1: [tex]\((10, 14)\)[/tex]
- Point 2: [tex]\((20, 19)\)[/tex]
2. Calculate the Slope [tex]\( m \)[/tex] of the Line:
The slope formula is given by:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Substituting the given points:
[tex]\[ m = \frac{19 - 14}{20 - 10} = \frac{5}{10} = \frac{1}{2} \][/tex]
3. Determine the Y-Intercept [tex]\( c \)[/tex]:
The equation of a line in slope-intercept form is:
[tex]\[ y = mx + c \][/tex]
We can use one of the given points and the slope to find the y-intercept. Let's use the point [tex]\((10, 14)\)[/tex]:
[tex]\[ 14 = \frac{1}{2} \cdot 10 + c \][/tex]
Simplifying:
[tex]\[ 14 = 5 + c \][/tex]
[tex]\[ c = 14 - 5 \][/tex]
[tex]\[ c = 9 \][/tex]
4. Find the Value of [tex]\( y \)[/tex] When [tex]\( x = 0 \)[/tex]:
Since the y-intercept, [tex]\( c \)[/tex], is the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 9 \][/tex]
So the missing [tex]\( y \)[/tex]-value when [tex]\( x = 0 \)[/tex] is:
[tex]\[ y = 9 \][/tex]
The completed table is:
[tex]\[ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 0 & 9 \\ \hline 10 & 14 \\ \hline 20 & 19 \\ \hline \end{tabular} \][/tex]
### Part B: Report the Equation of the Line
The equation of the line in slope-intercept form is:
[tex]\[ y = \frac{1}{2} x + 7 \][/tex]
This equation is consistent with the given form and reflects the correct slope and y-intercept.
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. For trustworthy answers, visit IDNLearn.com. Thank you for your visit, and see you next time for more reliable solutions.