Question

Select all answers that are true

a
y=2x+6 and goes through (2,10)

b
2x+y=6 slope of 1 and goes through the point (1,5)

c
The line 3y-7x=12 has a slope of 7/3 and passes through the point (-9,-17) .

Answer 1

Let's evaluate each statement one by one.

**a**: The line \( y = 2x + 6 \) and goes through (2, 10).
- To check this, we can substitute \( x = 2 \) into the equation:
\[
y = 2(2) + 6 = 4 + 6 = 10
\]
This means that the point (2, 10) does lie on the line.
- **True**

**b**: The line \( 2x + y = 6 \) has a slope of 1 and goes through the point (1, 5).
- First, let's find the slope of the line. We can rewrite it in slope-intercept form (y = mx + b):
\[
y = -2x + 6
\]
The slope (m) is -2, not 1.
- Next, checking if the point (1, 5) is on the line:
\[
2(1) + 5 = 2 + 5 = 7 \quad \text{(not equal to 6, so the point is not on the line)}
\]
- **False**

**c**: The line \( 3y - 7x = 12 \) has a slope of \( \frac{7}{3} \) and passes through the point (-9, -17).
- First, we need to find the slope by rewriting it in slope-intercept form (y = mx + b):
\[
3y = 7x + 12 \Rightarrow y = \frac{7}{3}x + 4
\]
The slope is \( \frac{7}{3} \), which is correct.
- Now let's check if the point (-9, -17) is on the line by substituting:
\[
3(-17) - 7(-9) = -51 + 63 = 12 \quad \text{(this is correct)}
\]
- **True**

Based on the evaluations:
- **a** is True
- **b** is False
- **c** is True

The true statements are: **a** and **c**.