Answer
$y = \frac{5}{4}x - \frac{17}{4}$
or
$y = 1.25x - 4.25$
Work Step by Step
1. The pattern equation for a line is:
$y = mx + b$
2. ($1 ,-3$) is point 1, and ($5,2$) is point 2. Now, use the formula to calculate the slope of that line:
$m = \frac{\Delta y}{\Delta x} = \frac{y_2-y_1}{x_2-x_1} = \frac{2 - (-3)}{5 - 1} = \frac{5}{4}$
Equation: $y = \frac{5}{4}x + b$
3. Now we can use a point to solve for b.
Since, the line pass through $(5,2)$, we know that x = 5 and y = 2 is a solution for that equation, so we can substitute these values and solve for b.
$2 = \frac{5}{4}(5) + b$
** Multiplying all elements by $4$:
$(2 * 4) = 25 + 4b$
$8 = 25 + 4b$
$8 - 25 = 25 + 4b - 25$
$-17 = 4b$
$\frac{-17}{4} = b$
4. Now, rewrite the equation of the line, substituting the value for m and b:
$y = \frac{5}{4}x - \frac{17}{4}= 1.25x - 4.25$
