Question

A line passes through the point (4, –6) and has a slope of Negative three-fourths. Which is the equation of the line?

A y = negative three-fourths x minus 3
B y = negative three-fourths x minus 6
C y = negative 3 x minus three-fourths
D y = negative 6 x minus three-fourths

Answer 1

the answer is A

Explanation:

Hope this helps!

Answer 2

Option A

The equation of line is
`y = (-3)/(4)x - 3`

Solution:

Given that line passes through the point (4, –6) and has a slope of Negative three-fourths

Given point is (x, y) = (4, -6)

`slope = (-3)/(4)`

The equation of line passing through point (x, y) and slope "m" is given as:

y = mx + c ----- eqn 1

Where "m" is the slope of line and "c" is the y - intercept

Substitute (x, y) = (4, -6) and
`m = (-3)/(4)` in eqn 1

`-6 = (-3)/(4) * 4 + c\\\\-6 = -3 + c\\\\c = -6 + 3\\\\c = -3`

The required equation of line is given as:

`\text{ Substitute } m = (-3)/(4) \text{ and } c = -3 \text{ in eqn 1 }`

`y = (-3)/(4)x - 3`

Thus the equation of line is found