Write the equation of the line that passes through the points (1, 7) and (5, 15) using function notation.
y = 2x + 5
y = 4x + 8
f(x) = 2x + 5
f(x) = 4x + 8
slope = (15-7)/(5-1) = 8/4 = 2
f(x) = 2 x + b
now find b
7 = 2(1) + b so b = 5
so
f(x) = 2x + 5
Write the equation of the line that passes through the points (3, 6) and (4, 10) using function notation.
To find the equation of the line passing through the points (1, 7) and (5, 15) using function notation, we can use the slope-intercept form of a linear equation, which is y = mx + b.
First, we need to find the slope, m, of the line. The slope is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
Using the points (1, 7) and (5, 15):
m = (15 - 7) / (5 - 1)
m = 8 / 4
m = 2
Now that we have the slope, we can substitute it into the equation y = mx + b and use one of the given coordinates to solve for the y-intercept, b.
Using the point (1, 7):
7 = 2(1) + b
7 = 2 + b
b = 7 - 2
b = 5
Therefore, the equation of the line that passes through the points (1, 7) and (5, 15), using function notation, is:
f(x) = 2x + 5
To find the equation of the line that passes through the points (1, 7) and (5, 15) using function notation, we need to use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope (m) of the line using the formula:
m = (change in y) / (change in x)
= (y2 - y1) / (x2 - x1)
Using the coordinates of the two points: (1, 7) and (5, 15):
m = (15 - 7) / (5 - 1)
= 8 / 4
= 2
So, the slope (m) of the line is 2.
Next, we can substitute the slope (m) and one of the points (1, 7) into the slope-intercept form (y = mx + b) to find the y-intercept (b).
7 = 2(1) + b
7 = 2 + b
b = 7 - 2
b = 5
Now, we have the slope (m) and the y-intercept (b), so we can write the equation of the line:
y = 2x + 5
This equation represents the line that passes through the points (1, 7) and (5, 15) in function notation.