Answer:
The slope-intercept form of the equation of a line is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).
Given a point (x1, y1) and a slope m, we can use the point-slope form of the equation of a line which is:
y - y1 = m(x - x1)
In this case, the point is (5, 12) and the slope is 3/5.
So the equation of the line in point-slope form is:
y - 12 = (3/5)(x - 5)
To put this equation in slope-intercept form, we need to solve for y.
To do this, we can add 12 to both sides:
y = (3/5)x + (12 - (3/5)*5)
y = (3/5)x + 12 - 3
y = (3/5)x + 9
So the equation of the line that goes through the point (5, 12) with the slope m = 3/5 in slope-intercept form is y = (3/5)x + 9