The slope-intercept form of a line is given by the equation: y = mx + b, where m represents the slope and b represents the y-intercept.
In this case, we are given that the line passes through the point (3, -2) and has a slope of 5. We can substitute these values into the slope-intercept form to find the equation of the line.
Using the point-slope form:
y - y₁ = m(x - x₁), where (x₁, y₁) = (3, -2) and m = 5.
Substituting the values:
y - (-2) = 5(x - 3)
Simplifying:
y + 2 = 5x - 15
Now, let's rearrange the equation to the slope-intercept form:
y = 5x - 15 - 2
y = 5x - 17
Therefore, the equation of the line in slope-intercept form that fits the given conditions is y = 5x - 17.