Explanation:
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.
We are given that the line has a slope of –9 and passes through the point (1,–3). We can use this information to find the value of b.
First, we can use the point-slope form of the equation of a line to write the equation:
y - y1 = m(x - x1)
where x1 and y1 are the coordinates of the given point.
Substituting the values we know, we get:
y - (-3) = -9(x - 1)
Simplifying:
y + 3 = -9x + 9
Subtracting 3 from both sides:
y = -9x + 6
This is now in the slope-intercept form, with a slope of –9 and a y-intercept of 6.
Therefore, the equation of the line is y = -9x + 6.