Chapter 5.1, Problem 32P

Each pair of points lies on a line with the given slope. Find $x$ or $y$. $(5,y),(6,4);$ slope $=0$

To determine

To Find: The value of $y$ .

Answer to Problem 32P

The value of $y$ is $4$ .

Explanation of Solution

Slope: Slope of any line is the characteristic feature of the line that gives us the direction of the line. Slope is also defined as the rate change of its coordinate axes. That is if we take $y$ as dependent variable and $x$ as independent variable then the slope will define how $x-axis$ will change for all input values of $x$ . However, these input values of $x$ are known as the Domain of the function representing the line.

Formula Used:

  $\begin{array}{l}\text{Slope }\left(m\right)\text{of line passing through two Co-ordinate points}\\ \left(x_1,y_1\right)\text{and }\left(x_2,y_2\right)\text{is}\\ m=\frac{y_2-y_1}{x_2-x_1}\end{array}$

For the given Problem

  $\begin{array}{l}\text{We have,}\\ \left(x_1,y_1\right)=\left(5,y\right)\\ \left(x_2,y_2\right)=\left(6,4\right)\\ \text{Therefore, according to the formula used,}\\ m=\frac{4-y}{6-5}\\ \Rightarrow m=\frac{4-y}{1}\\ \Rightarrow m=4-y\\ \text{Also, we have given slope is 0}\\ \text{Therefore, we have,}\\ 4-y=0\\ \Rightarrow y=4\end{array}$