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A line passes through the points $(-1,10)$ and $(4,-10)$ . Write its equation in slope-intercept form. $\newline$ Write your answer using integers, proper fractions, and improper fractions in simplest form.

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Write a linear equation from two points

Full solution

Q. A line passes through the points

(-1,10)

and

(4,-10)

. Write its equation in slope-intercept form.

\newline

Write your answer using integers, proper fractions, and improper fractions in simplest form.

Identify Points and Slope: Step $1$ : Identify the given points and calculate the slope of the line. $\newline$ Given points: $(-1, 10)$ and $(4, -10)$ . $\newline$ Using the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ , $\newline$ $m = \frac{-10 - 10}{4 - (-1)}$ , $\newline$ $m = \frac{-20}{5}$ , $\newline$ $m = -4$ .
Find Y-Intercept: Step $2$ : Use one of the points and the slope to find the y-intercept, $b$ . Using the point $(4, -10)$ and the slope $m = -4$ in the equation $y = mx + b$ , $-10 = -4(4) + b$ , $-10 = -16 + b$ , $b = -10 + 16$ , $b = 6$ .
Write Equation in Form: Step $3$ : Write the equation of the line in slope-intercept form using the values of $m$ and $b$ . Substitute $m = -4$ and $b = 6$ into $y = mx + b$ , $y = -4x + 6$ .

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