Answer:
y=2x+1
Step-by-step explanation:
This question is looking for translating data points into a line in slope intercept form. This line will go through the points (1, 3), (2, 5), (3, 7), and (4, 9).
The first thing to do is to select two of these points and find the differences in their x and y values.
Chosen points: (1, 3), (4, 9)
Change in y-values:
9-3=6
Change in x-values:
4-1=3
Now that the change in the x and y values have been determined, the slope can be calculated by dividing the change in y-values by the change in x-values.
Calculating slope:
[tex]slope=\frac{6}{3} =2[/tex]
The slope is represented by m in slope intercept form. The equation for this line is y=2x+b currently, so the y-intercept (b) still needs to be calculated. To find the y-intercept, rearrange slope intercept form so that it is solving for b instead of y.
y=mx+b
b=y-mx
Now that the equation has been rearranged, the y-intercept can be solved for by using one of the four given points and the slope that was calculated.
Calculating y-intercept:
Chosen point: (1, 3)
b=y-mx
b=3-2(1)=3-2=1
So the y-intercept for this function is 1.
To write the equation in slope intercept form, use the calculated slope and y-intercept.
Slope intercept equation:
y=mx+b
y=2x+1
So the first blank will be the slope (2) and the second blank will be the y-intercept (1).
