Question

ractice
what is the equation of a line that passes through (0.5, 4.25) and (2, 18.5) and has a y-intercept of $-0.5$?

Explanation:

Step1: Recall slope-intercept form

The slope-intercept equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. We know $b = -0.5$, so the equation is $y = mx - 0.5$.

Step2: Solve for slope $m$

Use one of the given points, e.g., $(2, 18.5)$. Substitute $x=2$, $y=18.5$ into the equation:
$$18.5 = m(2) - 0.5$$
Add 0.5 to both sides:
$$18.5 + 0.5 = 2m$$
$$19 = 2m$$
Divide both sides by 2:
$$m = \frac{19}{2} = 9.5$$
Verify with the other point $(0.5, 4.25)$:
$y = 9.5(0.5) - 0.5 = 4.75 - 0.5 = 4.25$, which matches the point.

Step3: Write final equation

Substitute $m=9.5$ and $b=-0.5$ into the slope-intercept form.

Answer:

$y = 9.5x - 0.5$ (or $y = \frac{19}{2}x - \frac{1}{2}$)