Question

Find the equation of a line that is parallel to this line and passes through the point (4,0). Which of the following points are on this line?
You can choose more than if there are multiple answer

◽(5,4)

◽(3,2)

◽(1,12)

◽(3,-4)

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Answer 1

Answer: A and D

Step-by-step explanation:

To find the line that is parallel to the given line, we must find the slope of the original. Parallel lines NEVER touch or cross. That tells us the slope MUST be the same. To find the slope, we use the formula $y=\frac{y_2-y_1}{x_2-x_1}$.

$y=\frac{4-0}{0-(-1)} =\frac{4}{1} =4$

With the slope, we can form an equation for the line.

y=4x+b            [plug in given point]

0=4(4)+b         [multiply]

0=16+b            [subtract both sides by 16]

b=-16

Now that we have the y-intercept, we can find the equation.

y=4x-16

After plugging in each point into the equation, we know that A and D are correct points on the line.