Q8. - Algebra 1

Question

Write an equation of the line with the given conditions.

$\left(-3,4\right),\left(1,12\right)$

Step-by-Step Solution

Answer

The equation of the straight line for the given condition is $\mathit{y}\mathbf{=}\mathbf{2}\mathit{x}\mathbf{+}\mathbf{12}$.

Step 1. State the concept of a straight line.

The standard form of slope and intercept form of the straight line is $y=mx+c$.

Here, $m$ is the slope of the straight line and $c$ is the $y$-intercept of the equation.

Step 2. State the equation of a line slope-point form.

The standard form of two-point form of the straight line is $y-y_1=\left(\frac{y_2-y_1}{x_2-x_1}\right)\left(x-x_1\right)$.

Here, coordinates of two points from which the straight line passes.

$\begin{array}{l}\left(x_1,y_1\right)=\left(-3,4\right)\\ \left(x_2,y_2\right)=\left(1,12\right)\end{array}$

Step 3. Substitute the values to get the required equation.

Substitute the above values in the equation $y-y_1=\left(\frac{y_2-y_1}{x_2-x_1}\right)\left(x-x_1\right)$.

$$\begin{gathered} y-y_1=\left(\frac{y_2-y_1}{x_2-x_1}\right)\left(x-x_1\right) \\ y-4=\left(\frac{12-4}{1-\left(-3\right)}\right)\left(x-\left(-3\right)\right) \\ y-4=\frac{8}{4}\left(x+4\right) \\ y=2x+8+4 \\ y=2x+12 \end{gathered}$$

The equation of the straight line is $y=2x+12$.