Question

What is the slope-intercept form of the equation of the line that passes through the points (2,7) and (4, - 1)?

Answer 1

y = -4x + 15

Explanation:

m = -y₁ + y₂\-x₁ + x₂

Find the Rate of change [Slope] using the above formula:

-7 - 1\-2 + 4 = -4

Next, we use the Point-Slope Formula [y - y₁ = m(x - x₁)] to convert to Slope-Intercept Formula [y = mx + b]:

y + 1 = -4[x - 4]

y + 1 = -4x + 16

- 1 - 1

________________

`y = - 4x + 15`

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Answer 2

y = -4x + 15

Explanation:

Slope-intercept form is y = mx + b

m = slope (
`(y_(2) - y_(1))/(x_(2) - x_(1))`)

b = y-intercept (where the line crosses the y-axis)

It doesn't matter which coordinate pair you use for (x₁,y₁).

(x₁,y₁) = (2,7)

(x₂,y₂) = (4,-1)

`(-1 - 7)/(4 - 2)` Simplify

`(-8)/(2)` Simplify

-4 = your slope (m)

To get this information into slope-intercept form, you have to plug it into point-slope form, y - y₁ = m(x - x₁). It doesn't matter which coordinate pair you use for (x₁,y₁).

y - y₁ = m(x - x₁) Let's use (2,7) since it doesn't have negatives.

y - 7 = -4 (x - 2) Distribute

y - 7 = -4x + 8 Add 7 to both sides

y = -4x + 15

Check your answer by plugging both coordinate pairs in.

y = -4x + 15

7 = -4(2) + 15

7 = -8 + 15

7 = 7

and

-1 = -4(4) + 15

-1 = -16 + 15

-1 = -1