A line passes through the point 2, 8 and has a slope of −3.Write an equation in slope-intercept form for this line.

Sure, let's find the equation of the line in slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Given:

• The slope $m = -3$
• The line passes through the point $(2, 8)$

We can use the point-slope form of the equation of a line, which is $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the line.

Step-by-step solution:

1. Substitute the given point and slope into the point-slope form: $y - 8 = -3(x - 2)$

2. Distribute the slope on the right-hand side: $y - 8 = -3x + 6$

3. Isolate $y$ to get the equation in slope-intercept form: $y = -3x + 6 + 8$ $y = -3x + 14$

So, the equation of the line in slope-intercept form is: $y = -3x + 14$