graph: 9,7 8,6 7,8 7,7 5,7 5,8 4,8 3.5,8.5 2,9 1,9.5
Write an equation in slope-intercept form of the trend line. (1 point) Responses y=−58x+9 y equals negative Start Fraction 5 over 8 End Fraction x plus 9 y=−14x+9 y equals negative Start Fraction 1 over 4 End Fraction x plus 9 y=−14x y equals negative Start Fraction 1 over 4 End Fraction x y=1x+9
To find the equation of the trend line, we need to find the slope and y-intercept. We will use the formula for slope:
m = (y2 - y1)/(x2 - x1)
Let's choose two points from the given data: (9,7) and (1,9.5)
m = (7 - 9.5)/(9 - 1)
m = -2.5/8
m = -5/16
Now, let's use the slope-intercept form of a line:
y = mx + b
We can substitute the slope we found (-5/16) for m:
y = (-5/16)x + b
Now, let's choose one of the points from the given data to find the value of b. Let's use the point (9,7).
7 = (-5/16)(9) + b
7 = (-45/16) + b
To find b, we need to solve for it:
b = 7 + 45/16
b = (112 + 45)/16
b = 157/16
So the equation of the trend line in slope-intercept form is:
y = (-5/16)x + 157/16
choose the options for the problem
Apologies for the confusion. Let's go through the options given:
y = −58x + 9
y equals negative 5/8 x plus 9
y = −14x + 9
y equals negative 1/4 x plus 9
None of these equations match the one we derived, which is:
y = (-5/16)x + 157/16
Therefore, the correct equation in slope-intercept form of the trend line is not listed among these options.
To find the equation of the trend line in slope-intercept form, we need to calculate the slope and the y-intercept using the given points.
Step 1: Calculate the slope (m):
We can use the formula to calculate the slope between two points:
m = (y2 - y1) / (x2 - x1)
Let's choose two points from the given graph: (9,7) and (8,6).
m = (6 - 7) / (8 - 9) = -1
Step 2: Calculate the y-intercept (b):
We can use the slope-intercept form of a linear equation: y = mx + b. Rearranging the equation, we get:
b = y - mx
Let's choose one of the points from the graph, like (9,7).
b = 7 - (-1) * 9 = 7 + 9 = 16
Step 3: Write the equation in slope-intercept form:
Putting the values we calculated into the equation, we get:
y = mx + b
y = -1x + 16
So, the equation of the trend line in slope-intercept form is:
y = -1x + 16