Final answer:
The equation of line w that is parallel to line v and passes through point (-10,1) is y = -1/5 x + 1.
Step-by-step explanation:
To find the equation of line w that is parallel to line v with an equation y = − 1/5 x + 9 and passes through point (−10,1), we first recognize that parallel lines have the same slope. Therefore, the slope of line w will be the same as line v, which is − 1/5. We can then use the point-slope form of the equation of a line to plug in the point (−10,1).
The point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through. For line w, this becomes y - 1 = − 1/5(x + 10). Simplifying this, we get:
- y - 1 = − 1/5 x - 2
- y = − 1/5 x + 1
When we isolate y, the equation is in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. The final equation for line w is y = − 1/5 x + 1.