Final answer:
To write the equation of a line that passes through two points, use the slope-intercept form y = mx + b. Find the slope using (y2 - y1) / (x2 - x1) and substitute it along with one of the points into the equation to find the y-intercept. Thus, the equation of the line passing through (-2, 5) and (1, -4) is y = -3x - 1.
Step-by-step explanation:
To write the equation of a line that passes through two points, we can use the slope-intercept form of a linear equation, y = mx + b. The slope, m, can be found using the formula: m = (y2 - y1) / (x2 - x1). Let's use the points (-2, 5) and (1, -4) to find the slope:
m = (-4 - 5) / (1 - (-2)) = -9 / 3 = -3
Now that we have the slope, we can choose either point and substitute its coordinates into the equation to solve for the y-intercept, b. Let's use the point (-2, 5):
5 = -3(-2) + b
b = 5 - 6 = -1
Therefore, the equation of the line that passes through the points (-2, 5) and (1, -4) is y = -3x - 1.