Write the equation of the linear function that passes through the points (9,4) and (11,6)
y= (____) x+ (____)
First, we need to find the slope of the line passing through the points (9,4) and (11,6).
The formula for finding the slope of a line passing through two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
In this case, (x1, y1) = (9,4) and (x2, y2) = (11,6)
m = (6 - 4) / (11 - 9)
m = 2 / 2
m = 1
Now that we have the slope, we can use the point-slope form of the equation of a line to find the equation of the line passing through the points (9,4) and (11,6).
y - y1 = m(x - x1)
y - 4 = 1(x - 9)
y - 4 = x - 9
y = x - 5
Therefore, the equation of the linear function that passes through the points (9,4) and (11,6) is:
y = x - 5
write the equation of the linear function that passes through the points (1,-7) and (-4,4)
y= (___)x+(___)
First, we need to find the slope of the line passing through the points (1, -7) and (-4, 4).
The formula for finding the slope of a line passing through two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
In this case, (x1, y1) = (1, -7) and (x2, y2) = (-4, 4)
m = (4 - (-7)) / (-4 - 1)
m = 11 / -5
m = -11/5
Now that we have the slope, we can use the point-slope form of the equation of a line to find the equation of the line passing through the points (1, -7) and (-4, 4).
y - y1 = m(x - x1)
y - (-7) = -(11/5)(x - 1)
y + 7 = -(11/5)(x - 1)
y + 7 = -(11/5)x + 11/5
y = -(11/5)x + 11/5 - 7
y = -(11/5)x + 11/5 - 35/5
y = -(11/5)x - 24/5
Therefore, the equation of the linear function that passes through the points (1, -7) and (-4, 4) is:
y = -(11/5)x - 24/5