Question

Select all statements that are true:

a
The line y=-5x+8 has a slope of 5 and passes through the point (0,0)

b
The line x+2y=8 has a slope of -(1/2) and passes through (0,8)

c
The line y = -3x+1 has a slope of 3 and passes through (0,2)

d
The line 4y-2x=10 has a slope of 2 and passes through the point (-3,1)

Answer 1

Let's analyze each statement one by one:

a. The line \( y = -5x + 8 \):
- Slope: The slope is -5, not 5.
- Y-intercept: When \( x = 0 \), \( y = 8 \).
- The line does NOT pass through the point (0,0).
- **This statement is false.**

b. The line \( x + 2y = 8 \):
- To find the slope, we can rewrite it in slope-intercept form (y = mx + b):
\[ 2y = -x + 8 \]
\[ y = -\frac{1}{2}x + 4 \]
- Slope: The slope is \(-\frac{1}{2}\).
- To check if it passes through (0,8):
\[ y = 4 \text{ when } x = 0 \text{, so it does NOT pass through } (0, 8) \].
- **This statement is false.**

c. The line \( y = -3x + 1 \):
- Slope: The slope is -3, not 3.
- Y-intercept: When \( x = 0 \), \( y = 1 \), not 2.
- **This statement is false.**

d. The line \( 4y - 2x = 10 \):
- To find the slope, we can rewrite it in slope-intercept form:
\[ 4y = 2x + 10 \]
\[ y = \frac{1}{2}x + \frac{5}{2} \]
- Slope: The slope is \(\frac{1}{2}\), not 2.
- To check if it passes through (-3,1):
\[ 4(1) - 2(-3) = 4 + 6 = 10 \text{, which is true.} \]
- **This statement is false.**

None of the statements a, b, c, or d are true.