Question

Which equation represents the line with slope 1/4 that passes through (–4, 8)?

Answer 1

Answer:

$y = \frac{1}{4}x +9$

Step-by-step explanation:

Given

$(x,y) = (-4,8)$

$m = \frac{1}{4}$ --- slope

Required

Determine the line equation

This can be solved using:

$y - y_1 = m(x - x_1)$

Substitute values for m, x1 and yi.

$y - 8 = \frac{1}{4}(x - (-4))$

$y - 8 = \frac{1}{4}(x +4)$

$y - 8 = \frac{1}{4}x +1$

Add 8 to both sides

$y - 8+8 = \frac{1}{4}x +1+8$

$y = \frac{1}{4}x +9$

Answer 2

We want to see which equation represents the line with the desired characteristics.

The correct option is B: y = (1/4)*x + 9

We know that a general line is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Here we do know that our line must have a slope 1/4, replacing that in the general equation we get:

y = (1/4)*x + b

We also know that our line passes through (-4, 8).

This means that y = 8 when x = -4, replacing that in the equation we get:

8 = (1/4)*-4 + b

8 = -1 + b

8 + 1 =b = 9

Then the equation is:

y = (1/4)*x + 9

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