Question

directions: chose the equation that best matches the line on the graph.
15.
graph of a line on a coordinate plane
a. $y = 3x + 4$
b. $y = \frac{1}{3}x + 4$
c. $y = -3x + 4$
d. $y = -\frac{1}{3}x - 4$
16.
graph of a line on a coordinate plane
a. $y = \frac{4}{5}x - 1$
b. $y = -\frac{4}{5}x - 1$
c. $y = \frac{5}{4}x - 1$
d. $y = -\frac{5}{4}x - 1$

Explanation:

Question 15

Step1: Analyze Slope Sign

The line in graph 15 is increasing (from bottom left to top right), so slope \( m > 0 \). Eliminate C (\( m=-3 \)) and D (\( m=-\frac{1}{3} \)).

Step2: Analyze Slope Magnitude

The line is steep, so slope \( |m| \) is large. \( y = 3x + 4 \) (A) has \( m = 3 \), \( y=\frac{1}{3}x + 4 \) (B) has \( m=\frac{1}{3} \). A is steeper.

Step3: Check Y-Intercept

The line crosses y-axis at \( (0, 4) \), so y-intercept \( b = 4 \). A: \( y = 3x + 4 \) matches \( b = 4 \) and steep positive slope.

Step1: Analyze Slope Sign

The line in graph 16 is decreasing (from top left to bottom right), so slope \( m < 0 \). Eliminate A (\( m=\frac{4}{5} \)) and C (\( m=\frac{5}{4} \)).

Step2: Analyze Slope Magnitude and Y-Intercept

Y-intercept is \( (0, -1) \), so \( b = -1 \). Check slope: from \( (0, -1) \), moving 5 right and 4 down (or 4 right and 5 down? Wait, let's calculate. Take two points: \( (0, -1) \) and \( (5, -5) \)? Wait, no, let's see grid. From \( (0, -1) \), moving 5 units right (x+5) and 4 units down (y-4)? Wait, slope \( m = \frac{\Delta y}{\Delta x} \). If line goes from \( (0, -1) \) to \( (5, -5) \), \( \Delta y = -4 \), \( \Delta x = 5 \), so \( m = -\frac{4}{5} \). So \( y = -\frac{4}{5}x - 1 \) (B) matches. Or check D: \( m = -\frac{5}{4} \), which would be steeper. B has smaller \( |m| \), matching the line's slope.

Step3: Confirm Equation

B: \( y = -\frac{4}{5}x - 1 \) has \( m = -\frac{4}{5} \) (negative, decreasing) and \( b = -1 \) (matches y-intercept).

Answer:

A. \( y = 3x + 4 \)

Question 16