Chapter 4.1, Problem 55PFA

To determine

To Find: The y- intercept of the equation of the line passing through $\left(-1,5\right)$ and slope $5$ .

Answer to Problem 55PFA

The y-intercept of a line is 10 option ‘D’ is correct.

Explanation of Solution

Given information:

Line passing through $\left(-1,5\right)$ and slope $5$

Concept and Formula Used:

Equation of line passing through point and given slope $y-y_1=m\left(x-x_1\right)$ .

For y- intercept put x coordinate equal to 0.

Calculation:

It is given that line passing through $\left(-1,5\right)$ and slope $5$

Equation of line through point and given slope is

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ \text{where }\left(x_1,y_1\right)=\left(-1,5\right)\&m=5\\ y-\left(5\right)=5\left(x-\left(-1\right)\right)\\ y-5=5\left(x+1\right)\\ y-5=5x+5\left(\text{Distributive property}\right)\\ \text{For }y-\text{intercept put }x=0\\ y-5=5\left(0\right)+5\\ y-5=5\\ \text{Add 5 to both sides}\\ y-5+5=5+5\\ y=10\end{array}$

Conclusion:

The y-intercept of a line is 10 option ‘D’ is correct.