Answer:
i. The slope of the equation is -2.
ii. The y-intercept of the equation is 6.
Step-by-step explanation:
Hey there!
First, let's find the slope using the slope formula:
[tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
We are given the points in the form (x₁, y₁), (x₂, y₂), which means we can define our values for these coordinates:
Then, we can plug these into the slope formula:
[tex]\displaystyle m = \frac{0 - 2}{3 - 2}[/tex]
Now, let's simplify the fraction by evaluating the numerator and the denominator separately.
[tex]\displaystyle m = \frac{-2}{1}[/tex]
Finally, we can simplify this to a whole number since we are dividing by 1.
[tex]\displaystyle m = -2[/tex]
Now, we can find the y-intercept of the line using the point-slope equation:
[tex]\displaystyle y - y_1 = m(x - x_1)[/tex]
Plug in the known values:
[tex]\displaystyle y - 2 = -2(x - 2)[/tex]
Simplify by using the distributive property:
[tex]\displaystyle y - 2 = -2x + 4[/tex]
Add 2 to both sides:
[tex]\displaystyle y = -2x + 6[/tex]
This gives us the equation of the line in slope-intercept form, which means we can extract the y-intercept from this equation.
The base equation for slope-intercept form is:
[tex]y=mx+b[/tex],
where b is the y-intercept.
Therefore, the y-intercept of the equation is 6 and the slope of the equation is -2.
Answer:
Answer: Slope = -2, y-Intercept = (0,6)
Step-by-step explanation:
Given: Points (2,2) and (3,0)
Find: Slope of Line and y-Intercept
Plan: Find the Slope-Intercept Form using y = mx + b
Part 1. Find Slope m
m = △y/△x = (y1 - y2)/(x1 - x2) = (2 - 0)/(2 -3) = 2/-1= -2 ✅
Part 2. Find b
Using point(2,2) & y = mx + b => 2 = (-2)(2) + b or 2 = -4 + b substituting and simplifying => b = 6✅
Double Check: Reasonable/Recalculated ✅ ✅
Answer: Slope = -2, y-Intercept = (0,6)
