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A line passes through the points $(-1,-7)$ and $(7,1)$ . 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,-7)

and

(7,1)

. Write its equation in slope-intercept form.

\newline

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

Calculate Slope: Step $1$ : Identify the given points and calculate the slope of the line. $\newline$ Given points: $(-1, -7)$ and $(7, 1)$ . $\newline$ Using the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ , we calculate: $\newline$ $m = \frac{1 - (-7)}{7 - (-1)}$ $\newline$ $m = \frac{8}{8}$ $\newline$ $m = 1$
Find Y-Intercept: Step $2$ : Use one of the points and the slope to find the y-intercept, $b$ . Using the point $(7, 1)$ and the slope $m = 1$ , substitute into the equation $y = mx + b$ : $1 = 1(7) + b$ $1 = 7 + b$ $b = 1 - 7$ $b = -6$
Write Equation: Step $3$ : Write the equation of the line in slope-intercept form using the values of $m$ and $b$ . Substitute $m = 1$ and $b = -6$ into $y = mx + b$ : $y = 1x - 6$ Slope-intercept form: $y = x - 6$

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