Final answer:
To find the equation of the line passing through the points (-3,1) and (6,-4), use the slope-intercept form of a linear equation.
Step-by-step explanation:
To find the equation of the line passing through the points (-3,1) and (6,-4), we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
First, we need to find the slope (m) of the line. The slope can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the given points.
Let's calculate the slope:
m = (-4 - 1) / (6 - (-3)) = -5 / 9.
Now, we can substitute the slope and one of the given points (let's use (-3,1)) into the slope-intercept form to find the y-intercept (b):
1 = (-5/9)(-3) + b
b = -2/3.
Therefore, the equation of the line passing through the points (-3,1) and (6,-4) is y = (-5/9)x - 2/3.