Answer
$y = \frac{3}{2}x + \frac{5}{2}$
Work Step by Step
We are given the points $(1, 4)$ and the point $(-1, 1)$.
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:
$m = \frac{1 - 4}{-1 - 1}$
Subtract the numerator and denominator to simplify:
$m = \frac{-3}{-2}$
Divide the numerator and denominator by $-1$:
$m = \frac{3}{2}$
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:
$y - 4 = \frac{3}{2}(x - 1)$
Use distribution to simplify:
$y - 4 = \frac{3}{2}x - \frac{3}{2}$
To change this equation into point-intercept form, we need to isolate $y$. To isolate $y$, we add $4$ to each side of the equation:
$y = \frac{3}{2}x - \frac{3}{2} + 4$
Change $4$ into an equivalent fraction that has $2$ as its denominator so that both fractions have the same denominator:
$y = \frac{3}{2}x - \frac{3}{2} + \frac{8}{2}$
Add the fractions to simplify:
$y = \frac{3}{2}x + \frac{5}{2}$
Now, we have the equation of the line in slope-intercept form.
