Work out the equation of a line which has a gradient of 3 and passes through the point (-1,3)
You asked:
Find an equation of the line through the point \((-1, 3)\) with slope \(3\).
MathBot Answer:
Standard Form:
$$\begin{aligned}Ax + By + C = 0\end{aligned}$$$$\begin{aligned} \text{Slope} &= -\frac{A}{B} \\ -\frac{A}{B} &= \frac{3}{1} \\ A =& -3, B = 1 \end{aligned}$$$$\begin{aligned}-3 x + 1 y + C &= 0 \\ -3(-1) + 1(3) + C &= 0 \\ 3 + 3 + C &= 0 \\ 3 + C &= -3 \\ C &= -6 \end{aligned}$$An equation of the line in standard form is: $- 3 x + y - 6 = 0$.
Slope-Intercept Form:
$$\begin{aligned} y = mx+b\end{aligned}$$$$\begin{aligned}y &= 3x + b \\ 3 &= 3 \times -1 + b \\ 3 &= -3 + b \\ b &= 6 \end{aligned}$$The slope-intercept form of the line is: $y = 3 x + 6$.