line u has an equation of y - 5 = 2(x - 5). line v includes the point (-2, -3) and is parallel to line u…
line u has an equation of y - 5 = 2(x - 5). line v includes the point (-2, -3) and is parallel to line u. what is the equation of line v? write the equation in slope - intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
Answer
Explanation:
Step1: Identify the slope of line u
The equation of line u is in point - slope form (y - y_1=m(x - x_1)), where (m) is the slope. For the line (y - 5=2(x - 5)), the slope (m = 2). Since line v is parallel to line u, the slope of line v is also (m = 2).
Step2: Use the point - slope form to find the equation of line v
The point - slope form is (y - y_1=m(x - x_1)), and the line v passes through the point ((-2,-3)). Substitute (x_1=-2), (y_1 = - 3) and (m = 2) into the point - slope form: [y-(-3)=2(x - (-2))] [y + 3=2(x + 2)]
Step3: Convert to slope - intercept form
Expand the right - hand side: (y+3=2x + 4). Then subtract 3 from both sides to get the slope - intercept form (y=2x+1).
Answer:
(y = 2x + 1)