Final answer:
To find the linear equation for the line that passes through (3, 1) and (-1, -4), calculate the slope and use the point-slope form to determine the y-intercept. The resulting equation is y = (5/4)x - 11/4.
Step-by-step explanation:
The linear equation that describes the line passing through the points (3, 1) and (-1, -4) is found using the formula for the slope (m) of a line.
First, we calculate the slope with the formula m = (y2 - y1) / (x2 - x1), using the given points.
We get m = (-4 - 1) / (-1 - 3), which simplifies to m = 5/4.
Next, we use the slope-intercept form of a line, y = mx + b, and plug in one of the points to solve for the y-intercept (b).
Let's use the point (3, 1). We have 1 = (5/4)(3) + b, which simplifies to 1 = 15/4 + b.
Solving for b gives us b = 1 - 15/4 = -11/4.
So, the linear equation is y = (5/4)x - 11/4.