Question

in slope-intercept form, what is the equation of the line passing through the points (3, 17) and (7, 25)?
$y=2x-11$
$y=2x+11$
$y=-3x+26$
$y=-2x+23$

Explanation:

Step1: Calculate the slope

Given points $(x_1,y_1)=(3,17)$ and $(x_2,y_2)=(7,25)$, use slope formula:
$$m=\frac{y_2-y_1}{x_2-x_1}=\frac{25-17}{7-3}=\frac{8}{4}=2$$

Step2: Find y-intercept $b$

Use slope-intercept form $y=mx+b$, substitute $m=2$ and $(3,17)$:
$$17=2(3)+b$$
$$17=6+b$$
$$b=17-6=11$$

Step3: Write line equation

Substitute $m=2$ and $b=11$ into $y=mx+b$:
$$y=2x+11$$

Answer:

B. $y=2x+11$