Question

Write an equation of a line parallel to line EF in slope-intercept form that passes through the point (2, 6).

Answer 1

Given :- The equation of line EF is y = 1 over 2 x + 6. Write an equation of a line parallel to line EF in slope-intercept form that passes through the point (2, 6).

Solution :-

we have,

→ Equation of line EF = (1/2)x + 6 .

The given equation is slope-intercept form where the general form is,

• y = mx + b.
• where m is the slope and the y-intercept is b.

From the equation we get,

• m = 1/2 .
• b = 6.

Now, we know that,

• The slope of the parallel lines is equal .

So,

→ Slope of equation is also = (1/2).

Thus, using the slope-point form of the forming the equation,

• y - y₁ = m(x - x₁)

Substituting the given values,

→ y - 6 = (1/2)(x - 2)

→ 2y - 12 = x - 2

→ 2y - x = - 2 + 12

→ 2y - x = 10

→ 2y = (10 + x)

→ y = (1/2)[10 + x]

→ y = (x/2) + 5 . (Ans.)

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