Give the equation of the line parallel to a line through (-3, 4) and (-5, -6) that passes
through the origin.

Step-by-step explanation:

The equation of a straight line is expressed in the slope intercept form as

y = mx + c

Where m represents the slope

c represents the intercept.

The given line passes through (-3, 4) and (-5, -6)

The slope of the given equation is expressed as

(y2 - y1)/(x2 - x1)

y2 = - 6

y1 = 4

x2 = - 5

x1 = - 3

Slope, m = (-6 - 4)/(-5 - -3) = - 10/-2 = 5

The slope,m = 5

The line that is parallel to the given line passes through the point the origin (0,0)

If two lines are parallel, it means that they have the same slope. Therefore, the slope of the line that is parallel to the given line is 5

To determine the intercept c, we will substitute m = 5, x = 0 and x = 0into the slope intercept equation. It becomes

= 5 × 0 + c

c = 0

The equation becomes

y = 5x + 0

y = 5x