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A line passes through the points (1,1)(1,1) and (2,8)(2,8). Write its equation in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.

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Full solution

Q. A line passes through the points (1,1)(1,1) and (2,8)(2,8). Write its equation in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.
  1. Calculate slope: Step 11: Calculate the slope of the line using the points (1,1)(1,1) and (2,8)(2,8). Slope formula: m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1} m=8−12−1m = \frac{8 - 1}{2 - 1} m=71m = \frac{7}{1} m=7m = 7
  2. Find y-intercept: Step 22: Use the slope m=7m = 7 and one of the points, say (1,1)(1,1), to find the y-intercept bb. Using the slope-intercept equation y=mx+by = mx + b, substitute x=1x = 1, y=1y = 1, and m=7m = 7. 1=7(1)+b1 = 7(1) + b 1=7+b1 = 7 + b b=1−7b = 1 - 7 (1,1)(1,1)00
  3. Write equation: Step 33: Write the equation of the line in slope-intercept form using the slope m=7m = 7 and y-intercept b=−6b = -6. Equation: y=mx+by = mx + b y=7x−6y = 7x - 6

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