Question

3. Write an equation in point-slope form for the line through the given point with the given slope.

(4, -6); m = 3/5

A. Y-4=3/5x (x+6)
B. Y+6=3/5(x-4)
C. Y+6=3/5x-4
D. Y-6=3/5(x+4)

Answer 1

B

Explanation:

recall that point-slope form of a linear equation is expressed as follows

y - y1 = m (x - x1)

where m = slope and (x1, y1) is the coordinate of any point on the line

so, here we have m = (3/5), x1 = 4 and y1 = -6

substitute these into the formula

y - (-6) = (3/5) (x - 4)

y + 6 = (3/5) (x - 4)----> answer

Answer 2

`\boxed{\text{B. }y + 6 =(3)/(5)(x - 4)}`

Explanation:

The point-slope formula for a straight line is

`y - y_(1) = m(x - x_(1))`

x₁ = 4; y₁ = -6; m = ⅗

Substitute the values

`\begin{array}{rcl}y - (-6) & = & (3)/(5)(x - 4)\\\\y + 6 & = & (3)/(5)(x - 4)\\\\\end{array}\\\text{The equation for the line is $\boxed{\mathbf{y + 6 =(3)/(5)(x - 4)}}$}`

The figure shows the graph of the equation with slope ⅗ passing through (4,-6).