Question

Write an equation in slope-intercept form of the line that passes through the point and has the given slope. $$ (8,4), m=-5 $$

Short answer

The equation of the line in slope-intercept form that passes through the point (8,4) with a slope of -5 is \(y = -5x + 44\).

Step-by-step solution

Use the given point and slope

In the equation \(y = mx + b\), substitute x and y with the values from the given point, and m with the slope. This will look like \(4 = -5 \cdot 8 + b\).

Solve for b

After making the substitutions in step one, solve for 'b'. Start by multiplying to get: \(4 = -40 + b\). Then add 40 to both sides of the equation to solve for 'b': \(b = 44\).

Write the final equation

Now that we have our slope and y-intercept, we can write the equation in slope-intercept form: \(y = -5x + 44\).