Answer:
To write the equation of a line in slope-intercept form, we need to find the slope (m) and the y-intercept (b).
Step 1: Find the slope (m)
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the given points (2,3) and (1,9), we can substitute the values into the formula to find the slope:
m = (9 - 3) / (1 - 2)
m = 6 / -1
m = -6
Step 2: Find the y-intercept (b)
The y-intercept is the value of y when x = 0. To find the y-intercept, we can use one of the given points. Let's use the point (2,3):
y = mx + b
3 = -6(2) + b
3 = -12 + b
b = 3 + 12
b = 15
Step 3: Write the equation in slope-intercept form
Now that we have the slope (m = -6) and the y-intercept (b = 15), we can write the equation in slope-intercept form, which is y = mx + b:
y = -6x + 15
So, the equation of the line passing through the points (2,3) and (1,9) in slope-intercept form is y = -6x + 15.
Explanation: