What is the equation of the line that passes through the point (-2,10) and is parallel to the line y = -4x - 3?
+26400 What is the equation of the line that passes through the point (-2,10) and is parallel to the line y = -4x - 3?
\(\begin{array}{rcl} \boxed{~ \begin{array}{rcl} y &=& m\cdot x +b \\ \end{array} ~}\\ (1) & x_1 &=& -2 \\ & y_1 &=&10\\ \hline & y_1 &= &m \cdot x_1 + b\\ & 10 &= &m \cdot (-2) + b\\ \hline (2) & y &=& -4x-3\\ & \text{slope } m &=& -4 \qquad \text{parallel line}\\ &\mathbf{m} &\mathbf{=}& \mathbf{4}\\ \hline & 10 &= &(-4) \cdot (-2) + b\\ & 10 &= &8 + b\\ &2 &= & b\\ &\mathbf{b} &\mathbf{=}& \mathbf{2}\\ \hline \boxed{~ \begin{array}{rcl} y &=& m\cdot x +b \\ y &=& -4x + 2 \end{array} ~} \end{array}\)
+26400 What is the equation of the line that passes through the point (-2,10) and is parallel to the line y = -4x - 3?
\(\begin{array}{rcl} \boxed{~ \begin{array}{rcl} y &=& m\cdot x +b \\ \end{array} ~}\\ (1) & x_1 &=& -2 \\ & y_1 &=&10\\ \hline & y_1 &= &m \cdot x_1 + b\\ & 10 &= &m \cdot (-2) + b\\ \hline (2) & y &=& -4x-3\\ & \text{slope } m &=& -4 \qquad \text{parallel line}\\ &\mathbf{m} &\mathbf{=}& \mathbf{4}\\ \hline & 10 &= &(-4) \cdot (-2) + b\\ & 10 &= &8 + b\\ &2 &= & b\\ &\mathbf{b} &\mathbf{=}& \mathbf{2}\\ \hline \boxed{~ \begin{array}{rcl} y &=& m\cdot x +b \\ y &=& -4x + 2 \end{array} ~} \end{array}\)
