Final answer:
The equation of the line that passes through the points –(3, –5) and –(2, –4) is y = x - 2, found by first calculating the slope and then using the point-slope form of a line's equation.
Step-by-step explanation:
To find the equation of a line that passes through the points –(3, –5) and –(2, –4), you first need to determine the slope of the line. The slope –(m) is calculated by the formula –(m = (y2–y1)/(x2–x1)) where (x1, y1) and (x2, y2) are the coordinates of the two points. Substituting the given points into the formula gives:
m = (–4 – (–5))/((–2) – (–3)) = 1/1 = 1
Now that we have the slope, we use the point–slope form of the equation of a line, which is y – y1 = m(x – x1). Using the slope we found and one of the given points, the equation is:
y – (–5) = 1(x – (–3))
Finally, simplify to get the standard form of the line's equation:
y = x – 2