Chapter 9.7, Problem 30STP

To determine

To determine the line that passes through the given point and is parallel to the line graphed.

Answer to Problem 30STP

The correct option is A.

Explanation of Solution

Given:

Four lines as follows:

1. $y=2x+1$
2. $y=2x+3$
3. $y=2x-5$
4. $y=-5x+8$

Concept used:

The equation of a straight line is given by $y=mx+c$ where, $m$ is the slope and $c$ is the y-intercept of the line.

Calculation:

The line passes through the point $\left(1,3\right)$ .

Discard the options one by one:

B. $y=2x+3$

At $x=1$ , $y=5$

Thus, the line $y=2x+3$ does not pass through $\left(1,3\right)$ .

C. $y=2x-5$

At $x=1$ , $y=-3$

Thus, the line $y=2x-5$ does not pass through $\left(1,3\right)$ .

The remaining options A, D pass through the point $\left(1,3\right)$ .

The line graphed has positive slope since the angle made with the positive x-axis is less than $90°$ Therefore, the line parallel to the graphed line must have positive slope.

The slope of the line $y=2x+1$ is $2$ which is positive while the line $y=-5x+8$ has negative slope $-5$ .

Hence, the correct option is A.