Find an equation of the line in point-slope form that passes through the point (2,4) and has a slope of 12.
You asked:
Find an equation of the line through the point \((2, 4)\) with slope \(12\).
MathBot Answer:
Standard Form:
$$\begin{aligned}Ax + By + C = 0\end{aligned}$$$$\begin{aligned} \text{Slope} &= -\frac{A}{B} \\ -\frac{A}{B} &= \frac{12}{1} \\ A =& -12, B = 1 \end{aligned}$$$$\begin{aligned}-12 x + 1 y + C &= 0 \\ -12(2) + 1(4) + C &= 0 \\ -24 + 4 + C &= 0 \\ 4 + C &= 24 \\ C &= 20 \end{aligned}$$An equation of the line in standard form is: $- 12 x + y + 20 = 0$.
Slope-Intercept Form:
$$\begin{aligned} y = mx+b\end{aligned}$$$$\begin{aligned}y &= 12x + b \\ 4 &= 12 \times 2 + b \\ 4 &= 24 + b \\ b &= -20 \end{aligned}$$The slope-intercept form of the line is: $y = 12 x - 20$.