Final answer:
The equation of the line that passes through the point (3, -3) with an intercept of (2, 4) is y = -7x + 18, determined by calculating the slope between the two points and using the point-slope form of a linear equation.
Step-by-step explanation:
To write an equation for a line that passes through the point (3, -3) and has an intercept of (2, 4), we need to determine the slope of the line using these two points. The slope (m) is calculated as the change in y divided by the change in x, which can be written as ∆y / ∆x or (y2 - y1) / (x2 - x1). Using our points: m = (4 - (-3)) / (2 - 3) = 7 / -1 = -7.
Now that we have the slope, we can use point-slope form to write the equation of our line: y - y1 = m(x - x1). Substituting one of the points and the slope we found: y - (-3) = -7(x - 3). Simplifying, we get y + 3 = -7x + 21. Finally, subtract 3 from both sides to get y = -7x + 18, which is the equation of the line.