Question

The line has a slope of -3/4 and passes through the point (5, 1). What is the point-slope form of the line? A) 3(y-1) = 4(x - 5) B) y + 1-3/4(x - 5) C) y-1-3/4(x + 5) D) y-1-3/4(x - 5)​

Answer 1

✦ Given that

• A line has a slope of -3/4 and passes through the point (5,1)

✦ We need to find

• The point-slope form of the line

`\hrulefill`

`\longleftrightarrow\rm{y-y_1=m(x-x_1)}`

`\longleftrightarrow\rm{y-1=-(3)/(4)(x-5)}`

Therefore the point slope form is y - 1 = -3/4(x - 5).

Answer 2

D) y-1-3/4(x - 5)

Explanation:

The point-slope form of a line is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. In this case, the slope of the line is -3/4 and the line passes through the point (5, 1). To find the point-slope form, we can substitute the values into the equation: y - 1 = -3/4(x - 5) This equation represents the line with a slope of -3/4 passing through the point (5, 1). So, the correct answer is D) y-1-3/4(x - 5).