Final answer:
To find the equation of a line that goes through two given points, we need to calculate the slope of the line using the formula (y2 - y1) / (x2 - x1) and then use the point-slope form of the equation. For the first line, the equation is y = -3x - 7, and for the second line, the equation is y = -3x + 7.
Step-by-step explanation:
To find the equation of a line that goes through two given points, we need to first calculate the slope of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Once we have the slope, we can use the point-slope form of the equation to write the equation of the line:
y - y1 = m(x - x1)
For the first line, using the points (2, -13) and (-2, -1), we have:
m = (-1 - (-13)) / (-2 - 2) = 12 / (-4) = -3
Substituting the values in the point-slope form, we get:
y - (-13) = -3(x - 2)
Simplifying the equation, we get:
y = -3x - 7
For the second line, using the points (5, -22) and (-3, 2), we have:
m = (2 - (-22)) / (-3 - 5) = 24 / (-8) = -3
Substituting the values in the point-slope form, we get:
y - (-22) = -3(x - 5)
Simplifying the equation, we get:
y = -3x + 7