Answer:
Explanation:
To find the equation of a line that passes through two given points, we can use the point-slope form of the equation of a line, which is:
y - y1 = m(x - x1)
where (x1, y1) is one of the given points, and m is the slope of the line.
First, we can find the slope of the line by using the two given points:
m = (y2 - y1)/(x2 - x1)
m = (8 - (-17))/(2 - (-3))
m = 25/5
m = 5
Now that we have the slope, we can use either of the two given points in the point-slope form of the equation of a line. Let's use the point (-3, -17):
y - y1 = m(x - x1)
y - (-17) = 5(x - (-3))
y + 17 = 5(x + 3)
This is the equation of the line in point-slope form. We can simplify it by distributing the 5:
y + 17 = 5x + 15
Then, we can solve for y by subtracting 17 from both sides:
y = 5x - 2
This is the equation of the line in slope-intercept form, where the slope is 5 and the y-intercept is -2. Therefore, the equation of the line that passes through the points (-3, -17) and (2, 8) is y = 5x - 2.