Explanation:
A line that is parallel to another line has the same slope but a different y-intercept. The slope of the line through the points (1,-2) and (-6,3) can be found using the slope-point formula:
slope = (y2 - y1) / (x2 - x1) = (3 - (-2)) / (-6 - 1) = 5/7
So, a line that is parallel to this line would have the same slope of 5/7. To find an equation for a line with this slope that passes through a different point, we can use the point-slope formula:
y - y1 = m * (x - x1)
Where m is the slope and (x1, y1) is a point on the line. We can choose any point to use in this formula, but a common choice is the origin (0,0). So, plugging in the values we have:
y - 0 = 5/7 * (x - 0)
y = 5/7 * x
This is the equation for a line that is parallel to the line through the points (1,-2) and (-6,3) and passes through the origin.