Write the equation of the linear function. Enter your answer in y=mx+b form?
x, y
2, 4
-3, -1
The slope, m, can be found using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) = (-3,-1) and (x2, y2) = (2,4)
m = (4 - (-1)) / (2 - (-3)) = 5/5 = 1
To find the y-intercept, b, we can use one of the given points. Let's use (2,4):
y = mx + b
4 = 1(2) + b
b = 2
Therefore, the equation of the linear function is:
y = x + 2
To find the equation of a linear function, we need to use the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
To find the slope (m):
m = (change in y / change in x)
Using the given points (2, 4) and (-3, -1):
change in y = (-1) - 4 = -5
change in x = (-3) - 2 = -5
m = -5 / -5 = 1
Now that we have the slope, we can find the y-intercept (b) by substituting the values of one of the given points into the equation y = mx + b.
Using the point (2, 4):
4 = (1)(2) + b
4 = 2 + b
4 - 2 = b
b = 2
Therefore, the equation of the linear function in y=mx+b form is:
y = 1x + 2