Question

please help :,) identify an equation in slope-intercept form for the line parallel to y=3x+5 that passes through (4,-1)

Answer 1

A. y + 1 = -3(x - 4)

Explanation:

If the equations are perpendicular, then that means they have the same slope, just with the opposite sign. In this case, the given equation's slope is 3, which means that the other equation's slope is -3. Now that we know the slope and one point, we can write the equation in point-slope form:

y - y1 = m(x - x1)

y - (-1) = -3(x - 4)

y + 1 = -3(x - 4)

The equation in point-slope form is answer choice A. y + 1 = -3(x - 4).

Hope this helps :)

Answer 2

The equation in point-slope form for the line perpendicular to
`$y=3x+5$` that passes through
`$(4,-1)$` is
`$y + 1 = -(1)/(3)(x - 4)$`.

Determine the slope of the original line: The coefficient of x in the equation
`$y=3x+5$` is 3.

Find the slope of the line perpendicular to the original line: The slope of a line perpendicular to another line is the negative reciprocal of its slope. So, the slope of the line perpendicular to y=3x+5 is
`$-(1)/(3)$`.

Use the point-slope form of a linear equation: The point-slope form is given by
`$y - y_1 = m(x - x_1)$`, where
`$(x_1, y_1)$` is a point on the line and m is the slope.

Substitute the values into the point-slope form: Substituting $(4,-1)$ as the point and
`$-(1)/(3)$` as the slope, we get
`$y - (-1) = -(1)/(3)(x - 4)$`.

Simplify the equation: Simplifying the equation gives
`$y + 1 = -(1)/(3)(x - 4)$`.

Therefore, the equation in point-slope form for the line perpendicular to y=3x+5 that passes through (4,-1) is:
`$y + 1 = -(1)/(3)(x - 4)$`.

So, the correct answer is option C.