Which of the following statements best describes the graph of 4x − y = 1?
It is a straight line joining the points (0, −1), (1, 3), and (−1, −5).
It is a straight line joining the points (4, −3), (−1, 2), and (−4, 5).
It is a curve joining the points (4, −1), (2, 3), and (4, 1).
It is a curve joining the points (0, −1), (−1, −3), and (1, 5).
its a
You know it is a line. Now just try the points in (a) and (b). Do they satisfy the equation?
is it a
To determine the correct statement that best describes the graph of 4x − y = 1, we need to understand the equation and use it to plot points.
The given equation, 4x − y = 1, is in slope-intercept form (y = mx + b) where m is the slope and b is the y-intercept. However, the equation is not in this form, so let's rearrange it:
4x − y = 1
Adding y to both sides:
4x = y + 1
Subtracting 1 from both sides:
4x - 1 = y
Now, the equation is in the form y = mx + b, where m represents the slope and b represents the y-intercept. We have:
y = 4x - 1
To find the points on the graph, we can assign values to x and solve for y. Let's choose a few values for x:
When x = 0:
y = 4(0) - 1
y = 0 - 1
y = -1
So, one point on the graph is (0, -1).
When x = 1:
y = 4(1) - 1
y = 4 - 1
y = 3
Another point on the graph is (1, 3).
When x = -1:
y = 4(-1) - 1
y = -4 - 1
y = -5
A third point on the graph is (-1, -5).
By plotting these three points on a coordinate plane, we can see that they form a straight line.
Comparing this with the given options:
- The first option states that the line passes through the points (0, -1), (1, 3), and (-1, -5), which matches our findings.
Therefore, the correct statement is: It is a straight line joining the points (0, −1), (1, 3), and (−1, −5).