Question

card 3
write an equation for each line graphed.
graph of two lines h (horizontal) and g (slanted) on a coordinate plane with x-axis from -4 to 4 and y-axis from -2 to 4

Explanation:

Step1: Analyze Line \( h \)

Line \( h \) is horizontal, so its slope \( m = 0 \). It intersects the \( y \)-axis at \( (0, 4) \), so the \( y \)-intercept \( b = 4 \). Using the slope - intercept form \( y=mx + b \), the equation for line \( h \) is \( y = 0x+4=4 \).

Step2: Analyze Line \( g \)

First, find the slope. Let's take two points on line \( g \). From the graph, when \( x = 0 \), \( y = 3 \) (so the \( y \)-intercept \( b = 3 \)), and when \( x = 4 \), \( y = 4 \). The slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{4 - 3}{4 - 0}=\frac{1}{4}\). Using the slope - intercept form \( y=mx + b \), the equation for line \( g \) is \( y=\frac{1}{4}x + 3 \).

Answer:

For line \( h \): \( y = 4 \)
For line \( g \): \( y=\frac{1}{4}x + 3 \)