Are these correct with the lines
y=0.15x+0.79
0.11x-y=-0.85
The line represents an estimate of the average cost of gasoline for each year. The line estimates the price of gasoline in January of each year (Bureau of Labor Statistics, 2006).
a)Do you expect the lines to be intersecting, parallel, or perpendicular? Explain your reasoning. I found that the lines are parallel
b)Use the equations of the lines to determine if they are parallel. What did you find?I found that the lines are parallel
c)Did your answer to part b confirm your expectation in part a?yes
The general formula for a straight line is
y = mx + b where m is the slope. Two lines must have the same slope if they are to be parallel.
In your first equation m = 0.15 (the coefficient of x is m).
Your second equation is
0.11x - y = -0.85 and rearranging we get
-y = -0.11x - 0.85 and multiply through by -1 gives
y = 0.11x + 0.85.
Check my work.
The slope in the second equation is 0.11 which isn't the same as m in equation #1; therefore, they can't be parallel.
To be perpendicular, the m values must be the negative reciprocal of each other (or said another way the product of the m values is -1). They are not so they can't be perpendicular. The only thing left is for them to intersect.
can someone please explain this question in more detail. I still do not get this.
To determine if the given lines are parallel, we can compare their slopes. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope.
For the first equation, y = 0.15x + 0.79, the slope is 0.15.
Now, let's rearrange the second equation, 0.11x - y = -0.85, into slope-intercept form.
Starting with 0.11x - y = -0.85, add y to both sides:
0.11x = y - 0.85
Then, rearrange the equation to isolate y:
y = 0.11x + 0.85
The slope of the second equation is 0.11.
Since the slopes of both equations are different (0.15 and 0.11), the lines represented by these equations are not parallel. Therefore, it appears that your answer to part b may be incorrect.
To further confirm, we can re-check the slopes of the equations and compare them. Given that they are different, it means the lines are not parallel.
Therefore, the correct answer for part a should be that the lines are not parallel.