Annie has created a graph of 3x+y=10 on the coordinate plane. Did Annie create her graph correctly?
Option 1: No; Annie's y
-intercept is correct but her slope is incorrect.
Option 2: No; Annie's slope is correct but her y
-intercept is incorrect.
Option 3: Yes; Annie's graph is correct.
Enter "1" for Option 1, "2" for Option 2, or "3" for Option 3.
Option 1: No; Annie's y-intercept is correct but her slope is incorrect.
Transform the linear equation 4x−8y=24 to slope-intercept form.(1 point)
Responses
−8y=−4x+24
negative 8 y equals negative 4 x plus 24
4x−8y−24=0
4 x minus 8 y minus 24 equals 0
4x−8y=24
4 x minus 8 y equals 24
y=12x−3
The linear equation 4x−8y=24 can be transformed into slope-intercept form as y=12x−3.
Write y−2=32(x+2) in slope-intercept form.(1 point)
Responses
y=32x+6
y equals Start Fraction 3 over 2 End Fraction x plus 6
y=32x+5
y equals Start Fraction 3 over 2 End Fraction x plus 5
y=32x+32
y equals Start Fraction 3 over 2 End Fraction x plus Start Fraction 3 over 2 End Fraction
y=32+5x
The equation y−2=32(x+2) can be written in slope-intercept form as y=32x+6.
Let's analyze the equation 3x + y = 10.
This equation is in standard form, which is in the form of Ax + By = C, where A, B, and C are constants.
To determine if Annie's graph is correct, we need to compare the equation to the standard slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.
By rearranging the equation 3x + y = 10, we get y = -3x + 10.
Comparing this to the standard slope-intercept form, we can see that the slope (m) is -3 and the y-intercept (b) is 10.
Now let's consider the options provided:
Option 1: No; Annie's y-intercept is correct but her slope is incorrect.
Option 2: No; Annie's slope is correct but her y-intercept is incorrect.
Option 3: Yes; Annie's graph is correct.
Based on our analysis, the correct answer is Option 3: Yes; Annie's graph is correct.
To determine if Annie created her graph correctly, we need to check if the equation 3x+y=10 is satisfied by the points on her graph.
The equation 3x+y=10 is in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Comparing the given equation with the slope-intercept form, we can see that the slope is 3 and the y-intercept is 10.
Annie's graph is said to be correct if it represents the equation correctly.
To verify this, we need to check if any point on Annie's graph satisfies the equation 3x+y=10.
If we pick a point on her graph, let's say (x, y), we can substitute the x and y values into the equation and check if it holds true.
For example, let's say we pick a point (2, 4) on Annie's graph.
Substituting x=2 and y=4 into the equation 3x+y=10, we get:
3(2) + 4 = 10
6 + 4 = 10
10 = 10
Since 10 equals 10, we can conclude that the point (2, 4), which lies on Annie's graph, satisfies the equation 3x+y=10.
Hence, Annie's graph is correct.
Therefore, the correct option is:
Option 3: Yes; Annie's graph is correct.