Question

Write the equation of the line that passes through the given points. (0, -1) and ( - 13, -4)

Answer 1

Linear Equations

We typically write linear equations in slope-intercept form:

$y=mx+b$

• m = slope
• b = y-intercept (the value of y when x=0)

Solving the Question

We're given:

• Line passes through (0, -1) and ( -13, -4)

1) Determine the slope (m)

To find the slope, we can use the slope equation:

$m=\dfrac{y_2-y_1}{x_2-x_1}$ where $(x_1,y_1)$ and $(x_2,y_2)$ are two points through which the line passes

⇒ Plug in the given points:

$m=\dfrac{-1-(-4)}{0-(-13)}\\\\m=\dfrac{-1+4}{0+13}\\\\m=\dfrac{3}{13}$

Therefore, the slope of the line is $\dfrac{3}{13}$. Plug this into $y=mx+b$:

$y=\dfrac{3}{13}x+b$

1) Determine the y-intercept (b)

In this case, the y-intercept is already given to us.

The y-intercept is the value of y when x=0. Given that the line passes through (0,-1), we know that this is -1.

Plug this into $y=\dfrac{3}{13}x+b$:

$y=\dfrac{3}{13}x+(-1)\\\\y=\dfrac{3}{13}x-1$

Answer

$y=\dfrac{3}{13}x-1$