Complete the equation of the line through $(-8,-2)$ and $(-4,6)$ . Use exact numbers. $\newline$ $y=\square$

Full solution

Q. Complete the equation of the line through

(-8,-2)

and

(-4,6)

. Use exact numbers.

\newline

y=\square

Calculate slope using formula: Calculate the slope ( extit{m}) of the line using the formula extit{m} = \frac{(y_2 - y_1)}{(x_2 - x_1)} with the given points $(-8, -2)$ and $(-4, 6)$ . $\newline$ \textit{m} = \frac{( $6$ - ( $-2$ ))}{( $-4$ - ( $-8$ ))} $\newline$ \textit{m} = \frac{( $6$ + $2$ )}{( $-4$ + $8$ )} $\newline$ \textit{m} = \frac{ $8$ }{ $4$ } $\newline$ \textit{m} = $2$
Find y-intercept using point-slope form: Use one of the points and the slope to find the y-intercept ( $b$ ) of the line. We can use the point-slope form $y - y_1 = m(x - x_1)$ and substitute the values. $\newline$ Let's use the point ( $-8$ , $-2$ ). $\newline$ $-2 - y_1 = 2(-8 - x_1)$ $\newline$ Since $y_1$ is $-2$ and $x_1$ is $-8$ , we have: $\newline$ $-2 - (-2) = 2(-8 - (-8))$ $\newline$ $y - y_1 = m(x - x_1)$ $0$ $\newline$ $y - y_1 = m(x - x_1)$ $1$ $\newline$ This step doesn't give us the value of $b$ directly, so we need to use the slope-intercept form $y - y_1 = m(x - x_1)$ $3$ with the same point to find $b$ . $\newline$ $y - y_1 = m(x - x_1)$ $5$ $\newline$ $y - y_1 = m(x - x_1)$ $6$ $\newline$ $y - y_1 = m(x - x_1)$ $7$ $\newline$ $y - y_1 = m(x - x_1)$ $8$
Use slope-intercept form to find $b$ : Write the equation of the line in slope-intercept form using the slope $m$ and the y-intercept $b$ . $\newline$ The slope $m$ is $2$ and the y-intercept $b$ is $14$ , so the equation is: $\newline$ $y = mx + b$ $\newline$ $y = 2x + 14$