Write the equation of the line that passes through (-2, 6) and (2, 14) in slope-intercept form.
y = 2x - 2
y = 2x + 10
y = 0.5x + 7
y = 0.5x - 4

Solution:

Given that line passes through (-2, 6) and (2, 14).

We have, equation of line in slope-intercept form is y = mx + c.

Since line passes through (-2, 6)

⇒ 6 = -2m + c --- (1)

Also the line passes through (2, 14)

⇒14 = 2m + c --- (2)

(1) + (2)

⇒ 20 = 2c ⇒ c = 10

(1) - (2) ⇒ -8 = -4m ⇒ m = 2

Therefore, the required equation is y = 2x + 10

Option (ii) is the answer.

Aliter

Given that, (x\(_1\), y\(_1\)) = (−2, 6) and (x\(_2\), y\(_2\)) = (2, 14)

The two-point form of a line passing through these two points (x₁, y₁) and (x₂, y₂) is:

(y − y₁) = [(y₂ − y₁) (x − x₁)] / (x₂ − x₁)

⇒ (y − y₁) (x₂ − x₁) = (y₂ − y₁) (x − x₁)

Substitute the values of points (x₁, y₁) and (x₂, y₂)

(y − 6) (2 − {-2}) = (14 − 6) (x − {-2})

(y − 6) (4) = (8) (x + 2)

4y - 24 = 8x + 16

4y = 8x + 40

y = 2x + 10

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Write the equation of the line that passes through (-2, 6) and (2, 14) in slope-intercept form.

Summary:

The equation of the line that passes through (-2, 6) and (2, 14) in slope-intercept form is y = 2x + 10.