Question

Select the coordinates that are parallel to

y=(3/4)x-6 and goes through (0,7)

There are two

a
(1,8)

b
(4,10)

c
(8,13)

d
(3,6)

Answer 1

To find the coordinates that are parallel to the line \( y = \frac{3}{4}x - 6 \) and go through the point \( (0, 7) \), we need to understand that parallel lines have the same slope.

The slope of the given line is \( \frac{3}{4} \). Therefore, any line parallel to it will also have a slope of \( \frac{3}{4} \).

Now, we can use the point-slope form of the line equation to find the equation of the line that goes through the point \( (0, 7) \) with this slope:

\[
y - y_1 = m(x - x_1)
\]
Substituting \( m = \frac{3}{4} \) and the point \( (0, 7) \):

\[
y - 7 = \frac{3}{4}(x - 0)
\]
\[
y - 7 = \frac{3}{4}x
\]
\[
y = \frac{3}{4}x + 7
\]

Now we can check which of the given points lie on the line \( y = \frac{3}{4}x + 7 \). We will substitute each point into the equation \( y = \frac{3}{4}x + 7 \):

1. For point \( a (1, 8) \):
\[
y = \frac{3}{4}(1) + 7 = \frac{3}{4} + 7 = \frac{3}{4} + \frac{28}{4} = \frac{31}{4} \approx 7.75 \quad (\text{not } 8)
\]

2. For point \( b (4, 10) \):
\[
y = \frac{3}{4}(4) + 7 = 3 + 7 = 10 \quad (\text{correct})
\]

3. For point \( c (8, 13) \):
\[
y = \frac{3}{4}(8) + 7 = 6 + 7 = 13 \quad (\text{correct})
\]

4. For point \( d (3, 6) \):
\[
y = \frac{3}{4}(3) + 7 = \frac{9}{4} + 7 = \frac{9}{4} + \frac{28}{4} = \frac{37}{4} \approx 9.25 \quad (\text{not } 6)
\]

The points that are parallel to the line and go through \( (0, 7) \) are:

- **b (4, 10)**
- **c (8, 13)**

So, the correct answers are **b** and **c**.