A line has a slope of -3 and passes through the point (-7,1). Write its equation in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form. ______

Identify slope-intercept form: Step 1: Identify the slope-intercept form of a line. The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Find y-intercept: Step 2: Use the given slope and point to find the y-intercept (b). Given slope (m) = -3 and point (-7, 1). Substitute into the equation: 1 = -3(-7) + b. Calculate: 1 = 21 + b. Solve for b: b = 1 - 21 = -20. Write line equation: Step 3: Write the equation of the line using the slope and y-intercept. Substitute m = -3 and b = -20 into y = mx + b. Equation: y = -3x - 20.

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A line has a slope of $-3$ and passes through the point $(-7,1)$ . 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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Math Problems

Grade 8

Write a linear equation from a slope and a point

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Q. A line has a slope of

-3

and passes through the point

(-7,1)

. Write its equation in slope-intercept form.

\newline

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

Identify slope-intercept form: Step $1$ : Identify the slope-intercept form of a line. $\newline$ The slope-intercept form is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
Find y-intercept: Step $2$ : Use the given slope and point to find the y-intercept $b$ . Given slope $m = -3$ and point $(-7, 1)$ . Substitute into the equation: $1 = -3(-7) + b$ . Calculate: $1 = 21 + b$ . Solve for $b$ : $b = 1 - 21 = -20$ .
Write line equation: Step $3$ : Write the equation of the line using the slope and y-intercept. $\newline$ Substitute $m = -3$ and $b = -20$ into $y = mx + b$ . $\newline$ Equation: $y = -3x - 20$ .