Question

Identify an equation in point-slope form for the line parallel to y = 3/4x - 4 that passes through (-1, 7).

Answer 1

the equation in point-slope form for the line parallel to y = (3/4)x - 4 that passes through (-1, 7) is 3x - 4y = -31.

Explanation:

To find the equation of a line parallel to another line, we need to use the same slope. The given line has a slope of 3/4.

Using the point-slope form of a line, which is given by:

y - y₁ = m(x - x₁)

where (x₁, y₁) represents the coordinates of a point on the line, and m represents the slope of the line, we can substitute the values (-1, 7) for (x₁, y₁) and 3/4 for m:

y - 7 = (3/4)(x - (-1))

Simplifying further:

y - 7 = (3/4)(x + 1)

Multiplying through by 4 to eliminate the fraction:

4(y - 7) = 3(x + 1)

Expanding:

4y - 28 = 3x + 3

Rearranging the equation to put it in standard form:

3x - 4y = -31

So, the equation in point-slope form for the line parallel to y = (3/4)x - 4 that passes through (-1, 7) is 3x - 4y = -31.

Answer 2

A)
`y-7=(3)/(4)(x+1)`

Explanation:

`y-y_1=m(x-x_1)\\y-7=(3)/(4)(x-(-1))\\y-7=(3)/(4)(x+1)`

Parallel lines must have the same slope, and then plugging in
`(x_1,y_1)=(-1,7)`, we easily get our equation.