find the equation of the line (2,-8) with gradient 5
You asked:
Find an equation of the line through the point \((2, -8)\) with slope \(5\).
MathBot Answer:
Standard Form:
$$\begin{aligned}Ax + By + C = 0\end{aligned}$$$$\begin{aligned} \text{Slope} &= -\frac{A}{B} \\ -\frac{A}{B} &= \frac{5}{1} \\ A =& -5, B = 1 \end{aligned}$$$$\begin{aligned}-5 x + 1 y + C &= 0 \\ -5(2) + 1(-8) + C &= 0 \\ -10 + -8 + C &= 0 \\ -8 + C &= 10 \\ C &= 18 \end{aligned}$$An equation of the line in standard form is: $- 5 x + y + 18 = 0$.
Slope-Intercept Form:
$$\begin{aligned} y = mx+b\end{aligned}$$$$\begin{aligned}y &= 5x + b \\ -8 &= 5 \times 2 + b \\ -8 &= 10 + b \\ b &= -18 \end{aligned}$$The slope-intercept form of the line is: $y = 5 x - 18$.