how would I write an equation for the following linear relationships:
(x5,y20),(x10,y30)(x15,y40)(x20,y50)(x25,y50)(x30,y50)
To write an equation for a linear relationship, you need to determine the slope and the y-intercept of the line. Here's how you can do it using the given data points:
Step 1: Identify two points from the given data. Let's choose (x5, y20) and (x30, y50).
Step 2: Calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
= (50 - 20) / (30 - 5)
= 30 / 25
= 6 / 5
= 1.2
Step 3: Use the slope-intercept form of a linear equation, which is:
y = mx + b
Step 4: Substitute one of the points' coordinates into the equation to determine the y-intercept (b). Let's use (x5, y20):
20 = 1.2(5) + b
20 = 6 + b
b = 20 - 6
b = 14
Step 5: Substitute the values of the slope (m = 1.2) and the y-intercept (b = 14) into the equation:
y = 1.2x + 14
So, the equation for the given linear relationship is y = 1.2x + 14.