Which equation would you use to find out if the two lines in the graph are parallel?
A coordinate graph is shown with 2 lines.Line a passes through a point with the label left parenthesis negative 2 comma 1 right parenthesis and a point with label left parenthesis 1 comma 4 right parenthesis.
Line b passes through a point with label left parenthesis negative 1 comma negative 1 right parenthesis and a point with label left parenthesis 3 comma 3 right parenthesis.
A. start fraction 4 minus 1 over negative 2 minus 1 end fraction equals start fraction 3 minus 1 over 3 minus 1 end fraction
B. start fraction 4 minus 1 over negative 2 minus 1 end fraction equals start fraction 3 minus left-parenthesis negative 1 right-parenthesis over 3 minus 1 end fraction
C. start fraction 4 minus 1 over 1 minus left-parenthesis negative 2 right-parenthesis end fraction equals start fraction 3 minus left-parenthesis negative 1 right-parenthesis over 3 minus left-parenthesis negative 1 right-parenthesis end fraction
D. start fraction 1 minus left-parenthesis negative 2 right-parenthesis over 4 minus 1 end fraction equals start fraction 3 minus 1 over 3 minus 1 end fraction
The correct equation to use to determine if two lines are parallel is the slope-intercept form of a line: y = mx + b, where m is the slope of the line.
To find if the two lines in the given graph are parallel, we need to calculate the slopes of each line and compare them.
For line a:
Slope = rise/run = (4-1)/(1-(-2)) = 3/3 = 1
For line b:
Slope = rise/run = (3-(-1))/(3-(-1)) = 4/4 = 1
Since both lines have the same slope (1), the two lines in the graph are parallel.
Therefore, the correct answer is not provided in the options.
To determine if the two lines in the graph are parallel, you need to compare the slopes of the two lines. If the slopes are equal, then the lines are parallel.
The slope-intercept form of a linear equation is y = mx + b, where m represents the slope of the line.
To find the slope of a line passing through two points (x1, y1) and (x2, y2), you can use the formula:
slope (m) = (y2 - y1) / (x2 - x1)
Now let's find the slopes of the two lines given in the problem.
Line a passes through the points (-2, 1) and (1, 4). Using the slope formula:
slope (line a) = (4 - 1) / (1 - (-2)) = 3 / 3 = 1
Line b passes through the points (-1, -1) and (3, 3). Using the slope formula:
slope (line b) = (3 - (-1)) / (3 - (-1)) = 4 / 4 = 1
Since the slopes of both lines are equal (slope a = slope b = 1), we can conclude that the lines are parallel.
Now let's go back to the given options:
A. (4 - 1) / (-2 - 1) = 3 / -3 = -1, which is not equal to 1.
B. (4 - 1) / (-2 - 1) = 3 / -3 = -1, which is not equal to 1.
C. (4 - 1) / (1 - (-2)) = 3 / 3 = 1, which is equal to 1.
D. (1 - (-2)) / (4 - 1) = 3 / 3 = 1, which is equal to 1.
Therefore, the equation you would use to find out if the two lines in the graph are parallel is option D:
start fraction 1 minus left-parenthesis negative 2 right-parenthesis over 4 minus 1 end fraction equals start fraction 3 minus 1 over 3 minus 1 end fraction.
To determine if two lines on a graph are parallel, you can use the slope-intercept form of the equation for each line. The slope-intercept form is y = mx + b, where m represents the slope of the line.
In this case, we need to find the equations of the lines passing through the given points and then compare their slopes to see if they are equal.
For line a, the two given points are (-2, 1) and (1, 4).
The slope (m) of line a can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
m = (4 - 1) / (1 - (-2))
m = 3 / 3
m = 1
So, the equation of line a is y = 1x + b.
Now, let's find the equation of line b passing through the points (-1, -1) and (3, 3).
Similarly, the slope (m) of line b can be calculated:
m = (3 - (-1)) / (3 - (-1))
m = 4 / 4
m = 1
So, the equation of line b is also y = 1x + b.
Comparing the equations of the two lines, we can see that their slopes are equal. Therefore, the correct equation to check if the lines are parallel is:
Option A: (4 - 1) / (-2 - 1) = (3 - 1) / (3 - 1)