Question

write an equation of the line that passes through (0, 10) and (6, 34)
y = 4x + 10
y = 6x + 34
y = 4
y = 6x - 4

Explanation:

Step1: Find slope of the line

The slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$. Using points $(0,10)$ and $(6,34)$:
$m=\frac{34-10}{6-0}=\frac{24}{6}=4$

Step2: Identify y-intercept

The line passes through $(0,10)$, so $b=10$.

Step3: Write line equation

Use slope-intercept form $y=mx+b$:
$y=4x+10$

Step4: Verify with second point

Substitute $x=6$ into $y=4x+10$:
$y=4(6)+10=24+10=34$, which matches $(6,34)$.

Answer:

A. $y = 4x + 10$