X Y
0 3
1 8
2 13
3 18
What is the equation of the line that contains the values given in the table?
A y = 5x + 3
B y = 5x − 37
C y = 5x − 87
D y = 1/5x + 63/5
y= m x + b
slope = 5/1 = m
y = 5 x + b
18 = 5 (3) + b
b = 3
so
y = 5 x + 3
check
3 = 3 (0) + 3
yes, caramba !
find the slope and the y-intercept
To determine the equation of the line that contains the values given in the table, we can examine the pattern and use the general equation for a straight line, which is:
y = mx + b
where:
- y is the value on the y-axis
- x is the corresponding value on the x-axis
- m is the slope of the line
- b is the y-intercept (the point where the line crosses the y-axis)
Looking at the given table, we can observe that the y-values increase by 5 each time the x-value increases by 1. This indicates that the slope (m) of the line is 5.
To find the y-intercept (b), we can substitute one of the points from the table into the general equation. Let's use the point (0, 3):
3 = 5(0) + b
3 = b
So, the y-intercept (b) is 3.
Now we can substitute the values of m and b into the general equation:
y = 5x + 3
Comparing this equation to the given options, we can see that the correct answer is:
A y = 5x + 3