Question

Select the coordinates that are parallel to the line

y=(-5/6)x-4 and goes through (-6,4)

There are two

a
(6,-6)

b
(-12,9)

c
(8,4)

d
(-5,2)

Answer 1

To find the coordinates that are parallel to the line given by the equation \(y = -\frac{5}{6}x - 4\) and pass through the point \((-6, 4)\), we need to remember that parallel lines have the same slope.

The slope of the given line is \(-\frac{5}{6}\). Therefore, any line parallel to it will also have this slope.

We can use the point-slope form of the equation of a line to find the equation of the line that goes through \((-6, 4)\):
\[
y - y_1 = m(x - x_1)
\]
where \(m\) is the slope, and \((x_1, y_1)\) is the point the line passes through.

Substituting the values:
\[
y - 4 = -\frac{5}{6}(x + 6)
\]

Now we need to simplify this equation:
\[
y - 4 = -\frac{5}{6}x - 5
\]
\[
y = -\frac{5}{6}x - 1
\]

Next, we can determine which of the given points satisfies the new line equation \(y = -\frac{5}{6}x - 1\).

Now, check each option:

a) \((6, -6)\):
\[
y = -\frac{5}{6}(6) - 1 = -5 - 1 = -6 \quad \text{(True)}
\]

b) \((-12, 9)\):
\[
y = -\frac{5}{6}(-12) - 1 = 10 - 1 = 9 \quad \text{(True)}
\]

c) \((8, 4)\):
\[
y = -\frac{5}{6}(8) - 1 = -\frac{40}{6} - 1 \approx -6.67 \quad \text{(False)}
\]

d) \((-5, 2)\):
\[
y = -\frac{5}{6}(-5) - 1 = \frac{25}{6} - 1 \approx 3.17 \quad \text{(False)}
\]

The points that are parallel to the original line and go through \((-6, 4)\) are:
- (6, -6)
- (-12, 9)

So the answers are **a** and **b**.