Final answer:
The equation of the line in slope-intercept form that passes through the point (-4,-6) with a slope of -5/2 is y = -5/2x + 4.
Step-by-step explanation:
To write the equation of a line in slope-intercept form, which is y = mx + b, we need to know the slope (m) and the y-intercept (b). The equation can be constructed using the slope and a point the line passes through.
In this case, we are given the slope as -5/2 and a point (-4, -6). We can use the point-slope form to first write the equation that incorporates the given point and then manipulate it into slope-intercept form. The point-slope form is (y - y1) = m(x - x1), where (x1, y1) is the given point. Substituting our values in, we get:
(y - (-6)) = -5/2(x - (-4))
Next, we distribute the slope on the right-hand side and simplify:
y + 6 = -5/2x - (-5/2 × 4)
y + 6 = -5/2x + 10
Now, to get the equation in slope-intercept form, we isolate y:
y = -5/2x + 10 - 6
y = -5/2x + 4
Therefore, the equation of the line in slope-intercept form is y = -5/2x + 4.