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Complete the equation of the line through $(-10,-7)$ and $(-5,-9)$

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Write a linear equation from two points

Full solution

Q. Complete the equation of the line through

(-10,-7)

and

(-5,-9)

Calculate slope: Calculate the slope $m$ of the line using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ with the given points $(-10,-7)$ and $(-5,-9)$ . $\newline$ $m = \frac{(-9 - (-7))}{(-5 - (-10))}$ $\newline$ $m = \frac{(-9 + 7)}{(-5 + 10)}$ $\newline$ $m = \frac{(-2)}{(5)}$ $\newline$ $m = -\frac{2}{5}$
Find y-intercept: Use one of the points and the slope to find the y-intercept $b$ of the line. Let's use the point $(-10, -7)$ and the slope $m = -\frac{2}{5}$ in the equation $y = mx + b$ . $\newline$ $-7 = \left(-\frac{2}{5}\right)(-10) + b$ $\newline$ $-7 = 4 + b$ $\newline$ $-7 - 4 = b$ $\newline$ $b = -11$
Write equation: Write the equation of the line in slope-intercept form using the slope $m$ and y-intercept $b$ . $y = mx + b$ $y = \left(-\frac{2}{5}\right)x + \left(-11\right)$ $y = \left(-\frac{2}{5}\right)x - 11$

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