Question

find the equation of the line specified.
the slope is 3, and it passes through (-4, -7).
a. y = 6x + 5 \t\t\tc. y = 3x - 7
b. y = 3x + 5 \t\t\td. y = 3x - 19

please select the best answer from the choices provided

○ a
● b
○ c
○ d

Explanation:

Step1: Recall point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \), where \( m \) is the slope and \( (x_1,y_1) \) is a point on the line. Given that \( m = 3 \) and the point \( (-4,-7) \), so \( x_1=-4 \) and \( y_1 = - 7 \).

Step2: Substitute values into point - slope form

Substitute \( m = 3 \), \( x_1=-4 \) and \( y_1=-7 \) into the point - slope formula:
\( y-(-7)=3(x - (-4)) \)
Simplify the left - hand side and the right - hand side:
\( y + 7=3(x + 4) \)

Step3: Expand and simplify

Expand the right - hand side: \( y+7 = 3x+12 \)
Subtract 7 from both sides of the equation: \( y=3x + 12-7 \)
\( y=3x + 5 \)

Answer:

b. \( y = 3x + 5 \)