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A line’s slope is −16. The line passes through the point (6,2). Find an equation for this line in both slope-intercept form and point-slope form using the given point. An equation for this line in slope-intercept form is: . An equation for this line in point-slope form is:

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Hello!

Here are how these forms are structured:

  • Slope-intercept form: y = mx + b
  • Point-slope form: y - y1 = m(x - x1)

In these forms, m is the slope, b is the y-intercept, and (x1, y1) is an ordered pair from the graph.

1. Slope-intercept form

To find the y-intercept, we have to substitute an ordered pair into the following equation: y = -16x + b, and solve for b.

2 = -16(6) + b

2 = -96 + b (add 96 to both sides)

98 = b

The slope-intercept form is y = -16x + 98

2. Point-slope form

Given a point from the graph and the slope, the equation will be very simple.

The point-slope form is y - 2 = -16(x - 6)

Final answers:

  • Slope-intercept form: y = -16x + 98
  • Point-slope form: y - 2 = -16(x - 6)

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