Answer:
The y-intercept (b) is - 5
The x-intercept is (5/3)
Explanation:
We are told this is a linear relationship, so lets look for a straight line equation in the form of y = mx + b, where m is the slope and b is the y-intercept, the goal of this question. Slope, m, is the Rise/Run, or rate of change, of the line. Calculate the slope by selecting any two points and find the Rise and Run. Let's use (2,1) and (7,16):
Rise = 16 - 1 = 15
Run = 7 - 2 = 5
Rise/Run (Slope, m) = 15/5 or 3
The equation becomes y = 3x + b.
To find the value of b, enter any of the given points for x and y and solve for b. Let's use point (2,1), since it makes the calculation easy:
y = 3x + b
1 = 3*2 + b for (2,1)
1 = 6 + b
b = -5
The y-intercept (b) is - 5. The full equation is y = 3x - 5
The x-intercept can be found by solving for x when the value of y is zero:
y = 3x - 5
0 = 3x - 5 for y = 0
-3x = -5
x = (5/3) The x-intercept is ((5/3),0)
See the attached graph.