Q19. - Algebra 1

Question

Write an equation of the line that passes through the given point and has the given slope.

$\left(1,2\right)$, slope 3

Step-by-Step Solution

Answer

The equation of the line that passes through the point $\left(1,2\right)$ and has the slope 3 is $y=3x-1$.

Step 1. Write the equation of the line that passes through the point x 1 , y 1 and has the slope m .

The equation of the line that passes through the point $\left(x_1,y_1\right)$ and has the slope $m$ is given by:

$y-y_1=m\left(x-x_1\right)$

Step 2. Write the equation of the line that passes through the point 1 , 2 and has the slope 3.

The slope of the line is 3. Therefore, the value of $m$ is 3.

The given point is $\left(1,2\right)$. Therefore, the values of $x_1$ and $y_1$ are 1 and 2 respectively.

Now substitute 3 for $m$, 1 for $x_1$ and 2 for $y_1$ in the equation $y-y_1=m\left(x-x_1\right)$ to find the equation of the line.

$$\begin{gathered} y-y_1=m\left(x-x_1\right) \\ y-2=3\left(x-1\right) \\ y-2=3x-3 \\ y=3x-3+2 \\ y=3x-1 \end{gathered}$$

Therefore, the equation of the line that passes through the point $\left(1,2\right)$ and has the slope 3 is $y=3x-1$.