What is the slope and the y-intercept of the equation 9+27/2x=−3/2y. Write the y-intercept as an ordered pair.(1 point)
The slope is ?. The y-intercept is (?).
To find the slope-intercept form of the given equation, we need to isolate y.
Starting with the given equation:
9 + 27/2x = -3/2y
First, let's get rid of the fractions by multiplying both sides of the equation by 2:
2(9 + 27/2x) = 2(-3/2y)
18 + 27x = -3y
Next, let's solve for y by dividing both sides of the equation by -3:
(18 + 27x)/(-3) = y
Simplifying this expression, we get:
-6 - 9x = y
So the slope-intercept form of the equation is:
y = -9x - 6
From this equation, we can see that the slope is -9 and the y-intercept is -6. Written as an ordered pair, the y-intercept is (0, -6).
Use the image to answer the question.
An illustration shows a coordinate plane with four quadrants. The x and y axes range from negative 10 to 10 in one unit increments. A downward slanting line is graphed on the coordinate plane. The downward slanting line passes through closed points plotted at left parenthesis 0 comma 10 right parenthesis and left parenthesis 1 comma 7 right parenthesis.
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.
To determine if Annie created her graph correctly, we need to compare her equation, 3x+y=10, to the information given in the illustration.
From the illustration, we can see that the line passes through the points (0,10) and (1,7).
We can use these points to check if Annie's equation is correct by substituting the x and y values into her equation.
For the point (0,10):
3(0) + y = 10
0 + y = 10
y = 10
For the point (1,7):
3(1) + y = 10
3 + y = 10
y = 7
Comparing these results with the y-values given in the illustration, we can see that Annie's equation is correct.
Therefore, the answer is Option 3: Yes; Annie's graph is correct.
To find the slope and y-intercept of the equation, we need to rewrite it into the standard form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Given equation: 9 + (27/2)x = -3/2y
Let's isolate y by dividing both sides of the equation by -3/2:
-3/2y = 9 + (27/2)x
Dividing both sides by -3/2:
y = (-2/3)(9 + (27/2)x)
Simplifying the equation:
y = (-2/3)(9) + (-2/3)((27/2)x)
y = -6 + (-9/2)x
Comparing the equation with the standard form, we can identify the slope (m) and y-intercept (b):
Slope (m) = -9/2
Y-intercept (b) = -6
Writing the y-intercept as an ordered pair, it would be (0, -6).
Therefore, the slope is -9/2 and the y-intercept is (0, -6).
To find the slope and y-intercept of the equation, we need to rewrite it in the standard form, which is in the form of y = mx + b, where m represents the slope and b represents the y-intercept.
Let's start by rearranging the given equation:
9 + (27/2)x = -(3/2)y
Multiply both sides of the equation by -2/3 to isolate y:
(-2/3)(9 + (27/2)x) = y
Simplifying both sides of the equation:
-6 - 18x = y
Now we have the equation in the form y = mx + b, where m is the slope and b is the y-intercept. So, we can identify that the slope (m) is -18 and the y-intercept (b) is -6.
Therefore, the slope is -18 and the y-intercept is (-6, 0).