Question

question 3
given the graph, write the equation of the line
graph of a line on a coordinate plane
options:
a) $y = x + \frac{4}{3}$
b) $y = \frac{1}{3}x - 1$
c) $y = -x + \frac{4}{3}$
d) $y = \frac{4}{3}x + 1$
e) $y = \frac{4}{3}x - 1$
choose the correct option from a, b, c, d, e

Explanation:

Step1: Analyze the slope

The line is increasing, so the slope \( m \) is positive. Let's pick two points, e.g., \( (0, 1) \) (y-intercept) and \( (3, 5) \) (since from \( x=0 \) to \( x=3 \), \( y \) goes from 1 to 5). The slope \( m=\frac{5 - 1}{3 - 0}=\frac{4}{3} \).

Step2: Analyze the y-intercept

The line crosses the y-axis at \( (0, 1) \), so the y-intercept \( b = 1 \).

Step3: Match with options

The slope-intercept form is \( y=mx + b \). With \( m=\frac{4}{3} \) and \( b = 1 \), the equation is \( y=\frac{4}{3}x + 1 \), which is option d.

Answer:

d) \( y=\frac{4}{3}x + 1 \)