Write an equation of the line passes through (4, 1) and is parallel to y=−2x+7.

Point-slope:

y - 1 = -2(x - 4)

Slope-intercept:

y = -2x + 9

Standard:

2x + y = 9

Step-by-step explanation:

The equation you were given is:

y = -2x + 7

This is slope-intercept form of the equation. When an eq is in this format you can see (no work!) the slope and the y-intercept (hence the name) Anyway, the number infrontof the x is the slope. Parallel lines have the same slope. So your new equation will also have a slope of -2.

We have a point on the new line, but not the y-intercept, so we need another form of the equation. Point-slope equation is something we can use.

y - y = m(x - x)

in this fill-in-the-blank formula, we put the slope in place of the m. And, given any point on the line (x,y) We fill in the SECOND x and the SECOND y. The FIRST x and y just stay variables.

So, we know the slope is -2.

And a point on the line is (4,1).

Fill in:

y - 1 = -2(x - 4)

This is the least- amount-of-work-for-us, equation of the line.

Sometimes the teacher/book/class/program asks for a specific version of the equation.

y - 1 = -2(x - 4)

Distribute the -2.

y - 1 = -2x + 8

Add 1 to both sides.

y = -2x + 9

This is slope-intercept form of the equation.

Or we can change it to Standard form.

y = -2x + 9

Add 2x to both sides.

2x + y = 9

c

step-by-step explanation:

there is vertical asymptote at x = 2 and x = 0

vertical asymptote occurs at the points where the denominator is 0. so we can say that

x = 2 occurs when there is a factor (x-2) in the denominator, and

x = 0 occurs when there is a factor "x" in the denominator

thus, the denominator of the equation would have "x * (x-2)", this is option c only. that's the correct answer.