write an equation of the line that passes through the given point and is parallel to the graph of the given equation.

Question

please help me answer (2, -1);y = 5x - 2

Answer 1

Hello, Quan,

Remember that the standard form of a line equation is y = mx + b. Since you need a line that is parallel to y = 5x - 2, the first thing to do is use the same slope (m), which is 5 in this case.

The new line would look like this: y = 5x + b. I use "b" instead of -2, since we'll calculate a "b" for the new line by substituting the given point of (2, -1) into y = 5x + b.

-1 = 5*(2) + b

b = -11

The parallel line that goes through (2,-1) is y = 5x - 11

The new line is the blue, on the right. Note that it is parallel to the original (green) line and also intersects at (2, -1). (Each chart is is 0.5 unit).

Bob

Answer 2

write an equation of the line that passes through the given point and is parallel to the graph of the given equation.

please help me answer (2, -1);y = 5x - 2

Given the point slope form or a line as:

y- y₁ = m (x - x₁) where m is the slope (x_1,y₁) is a point on the line we have......

y - (-1) = m (x - 2).......now the line is PARALLEL to the given line. Parallel lines have the SAME slope.

y + 2 = 5 (x - 2)

y + 2 = 5x - 10................point slope form of line...SIMPLIFIED.....

y = 5x - 12 subtract 2 from both sides.....slope intercept form of line.....Right?