Question

A line with a slope of 3/4 passes through (-4,-1). Write the equation of the line in standard form. A. 3x + 4y = 5 B. y + 1 = 3/4(x + 4) C. y = 3/4x + 2 D. 3x - 4y = - 8

Answer 1

Solution

$\begin{gathered} Given,\text{ } \\ slope,\text{ m=}\frac{3}{4} \\ (x_1,y_1)=(-4,-1) \end{gathered}$

Equation of a straight line given slope and one point can be determined by the formula

$\begin{gathered} y-y_1=m(x-x_1) \\ y-(-1)=\frac{3}{4}(x-(-4)) \\ y+1=\frac{3}{4}(x+4) \\ 4(y+1)=3(x+4) \\ 4y+4=3x+12 \\ 4y=3x+12-4 \\ 4y=3x+8 \\ Re-\text{arrange} \\ -8=3x-4y \\ 3x-4y=-8 \end{gathered}$

The answer is option D