## Algebra 1: Common Core (15th Edition)

$y = 0.25x + 1.875$
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.