Question

Find the slope and the y intercept of a line that passes through these points (2,2)and (3,0)

Answer 1

Answer: Slope = -2, y-Intercept = (0,6)

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)

Answer 2

i. The slope of the equation is -2.

ii. The y-intercept of the equation is 6.

Explanation:

Hey there!

First, let's find the slope using the slope formula:

`\displaystyle m = (y_2 - y_1)/(x_2 - x_1)`

We are given the points in the form (x₁, y₁), (x₂, y₂), which means we can define our values for these coordinates:

• x₁ = 2
• x₂ = 3
• y₁ = 3
• y₂ = 0

Then, we can plug these into the slope formula:

`\displaystyle m = (0 - 2)/(3 - 2)`

Now, let's simplify the fraction by evaluating the numerator and the denominator separately.

`\displaystyle m = (-2)/(1)`

Finally, we can simplify this to a whole number since we are dividing by 1.

`\displaystyle m = -2`

Now, we can find the y-intercept of the line using the point-slope equation:

`\displaystyle y - y_1 = m(x - x_1)`

Plug in the known values:

`\displaystyle y - 2 = -2(x - 2)`

Simplify by using the distributive property:

`\displaystyle y - 2 = -2x + 4`

Add 2 to both sides:

`\displaystyle y = -2x + 6`

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:

`y=mx+b`,

where b is the y-intercept.

Therefore, the y-intercept of the equation is 6 and the slope of the equation is -2.