Question

line gh passes through points (2, 5) and (6, 9). which equation represents line gh?
○ ( y = x + 3 )
○ ( y = x - 3 )
○ ( y = 3x + 3 )
○ ( y = 3x - 3 )

Explanation:

Step1: Calculate slope $m$

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
Substitute $(x_1,y_1)=(2,5)$, $(x_2,y_2)=(6,9)$:
$m=\frac{9-5}{6-2}=\frac{4}{4}=1$

Step2: Find y-intercept $b$

Use $y=mx+b$, substitute $m=1$, $(x,y)=(2,5)$:
$5=1\times2+b$
Solve for $b$: $b=5-2=3$

Step3: Write line equation

Substitute $m=1$, $b=3$ into $y=mx+b$:
$y=x+3$
Verify with $(6,9)$: $9=6+3$, which holds true.

Answer:

A. $y = x + 3$