Question

Select the points that are parallel to y = (-1/2)x-2 and goes through (8,10)

There are two

a
(0,1)

b
(2,13)

c
(6,10)

d
(-2,15)

Answer 1

To determine which points are parallel to the line given by the equation \( y = -\frac{1}{2}x - 2 \) and go through the point \( (8, 10) \), we first note the slope of the given line, which is \( -\frac{1}{2} \).

Lines that are parallel to this one will also have the same slope, \( -\frac{1}{2} \). Therefore, any line parallel to the given line can be expressed in the slope-intercept form as:

\[ y = -\frac{1}{2}x + b \]

To find the value of \( b \), we can use the point \( (8, 10) \) which lies on the parallel line:

1. Substitute \( x = 8 \) and \( y = 10 \) into the equation:
\[
10 = -\frac{1}{2}(8) + b
\]
\[
10 = -4 + b
\]
\[
b = 14
\]

So the equation of the line parallel to \( y = -\frac{1}{2}x - 2 \) and passing through \( (8, 10) \) is:

\[ y = -\frac{1}{2}x + 14 \]

Next, we can check each of the provided points to see if they lie on this line:

- For point **a (0, 1)**:
\[
y = -\frac{1}{2}(0) + 14 = 14 \quad \text{This point does not lie on the line.}
\]

- For point **b (2, 13)**:
\[
y = -\frac{1}{2}(2) + 14 = -1 + 14 = 13 \quad \text{This point lies on the line.}
\]

- For point **c (6, 10)**:
\[
y = -\frac{1}{2}(6) + 14 = -3 + 14 = 11 \quad \text{This point does not lie on the line.}
\]

- For point **d (-2, 15)**:
\[
y = -\frac{1}{2}(-2) + 14 = 1 + 14 = 15 \quad \text{This point lies on the line.}
\]

The points that are parallel to \( y = -\frac{1}{2}x - 2 \) and pass through \( (8, 10) \) are:

**b (2, 13)** and **d (-2, 15)**.