Question

Write the equation in slope-intercept form given (y=mx+b) given: (-6, 5) and (3, -1) 1st step: Find slope 2nd step: Use the point slope formula

Answer 1

To write the equation in slope-intercept form given two points, (-6, 5) and (3, -1), we first find the slope using the slope formula and then use the point-slope formula to write the equation.

Step-by-step explanation:

To write the equation in slope-intercept form (y = mx + b) given the points (-6, 5) and (3, -1), we first need to find the slope (m) and then use the point-slope formula.

1. Finding the slope: The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula: m = (y2 - y1) / (x2 - x1). Plugging in the coordinates: m = (-1 - 5) / (3 - (-6)) = -6 / 9 = -2/3.
2. Using the point-slope formula: We can use one of the given points and the slope to write the equation. Let's use the point (-6, 5). The point-slope formula is: y - y1 = m(x - x1). Plugging in the values, we get: y - 5 = (-2/3)(x - (-6)).
3. Converting to slope-intercept form: To convert the equation to slope-intercept form (y = mx + b), we need to solve for y and simplify. Distributing and rearranging the equation, we get: y = (-2/3)x + 4 + 5 = (-2/3)x + 9.

Therefore, the equation in slope-intercept form is y = (-2/3)x + 9.

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