Final answer:
To find the slope-intercept form of the line through the point (4,1) with a slope of -6, substitute the slope and point into the point-slope equation and solve for y to get the final form y = -6x + 25.
Step-by-step explanation:
The student is asking how to find the slope-intercept form of the equation of the line that passes through the point (4,1) with a slope of -6. The slope-intercept form is generally expressed as y = mx + b, where m is the slope and b is the y-intercept.
Since the slope (m) is given as -6 and we have a point on the line (4,1), we can substitute these values into the slope-intercept form:
y - y1 = m(x - x1)
y - 1 = -6(x - 4)
Next, distribute -6 to both terms in the parenthesis:
y - 1 = -6x + 24
Finally, add 1 to both sides to find the y-intercept (b):
y = -6x + 25
Thus, the slope-intercept form of the line is y = -6x + 25.