Answer
$y = 0.25x + 1.875$
Work Step by Step
We are given the points $(0.5, 2)$ and $(4.5, 3)$.
Let's use the formula to find the slope $m$ given two points:
$m = \frac{y_2 - y_1}{x_2 - x_1}$
Let's plug in the values into this formula:
$m = \frac{3 - 2}{4.5 - 0.5}$
Subtract the numerator and denominator to simplify:
$m = \frac{1}{4}$
Now that we have the slope, we can use one of the points and plug these values into the point-slope equation, which is given by the formula:
$y - y_1 = m(x - x_1)$
Let's plug in the points and slope into the formula:
$y - 2 = \frac{1}{4}(x - 0.5)$
This equation is now in point-slope form. To change this equation into point-intercept form, we need to isolate $y$.
Use distribution to simplify:
$y - 2 = \frac{1}{4}x - \frac{1}{4}(0.5)$
Simplify by multiplying:
$y - 2 = \frac{1}{4}x - 0.125$
To isolate $y$, we add $2$ to each side of the equation:
$y = \frac{1}{4}x - 0.125 + 2$
Add to simplify:
$y = \frac{1}{4}x + 1.875$
Let's change $\frac{1}{4}$ into a decimal to be consistent:
$y = 0.25x + 1.875$
Now, we have the equation of the line in slope-intercept form.
