A line passes through the points (1,1) and (2,7). Write its equation in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form. ______

Calculate slope: Step 1: Calculate the slope of the line using the points (1,1) and (2,7). Slope formula: m = (y2 - y1) / (x2 - x1) Calculation: m = (7 - 1) / (2 - 1) = 6 / 1 = 6Find y-intercept: Step 2: Use the slope (m = 6) and one of the points, say (1,1), to find the y-intercept (b). Using the slope-intercept form equation y = mx + b, substitute x = 1, y = 1, and m = 6. 1 = 6(1) + b 1 = 6 + b b = 1 - 6 b = -5Write equation: Step 3: Write the equation of the line in slope-intercept form using the slope (m = 6) and y-intercept (b = -5). Equation: y = 6x - 5

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A line passes through the points $(1,1)$ and $(2,7)$ . 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 two points

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Q. A line passes through the points

(1,1)

and

(2,7)

. Write its equation in slope-intercept form.

\newline

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

Calculate slope: Step $1$ : Calculate the slope of the line using the points $(1,1)$ and $(2,7)$ . Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Calculation: $m = \frac{7 - 1}{2 - 1} = \frac{6}{1} = 6$
Find y-intercept: Step $2$ : Use the slope $m = 6$ and one of the points, say $(1,1)$ , to find the y-intercept $b$ . Using the slope-intercept form equation $y = mx + b$ , substitute $x = 1$ , $y = 1$ , and $m = 6$ . $1 = 6(1) + b$ $1 = 6 + b$ $b = 1 - 6$ $(1,1)$ $0$
Write equation: Step $3$ : Write the equation of the line in slope-intercept form using the slope $m = 6$ and y-intercept $b = -5$ . Equation: $y = 6x - 5$