Find the equation of the line in slope-intercept form.
Slope is −4, and (9,5) is on the line.
well, we know it is
y = -4 x + b
so all we need is b
5 = -4(9) + b
5 = -36 + b
b = 41
so
y = -4 x + 41
y = -4x + 41 <--- is the equation ?
well, check it and see.
To find the equation of a line in slope-intercept form, we need two pieces of information: the slope and a point on the line.
Given that the slope is -4 and the point (9,5) is on the line, we can use the point-slope form of an equation to find the equation of the line.
The point-slope form of an equation is:
y - y1 = m(x - x1)
Where:
- (x1, y1) is the given point on the line.
- m is the slope of the line.
Using the values we know, (x1, y1) = (9, 5) and m = -4, we can substitute these values into the point-slope form:
y - 5 = -4(x - 9)
Now, we can simplify the equation by distributing -4 into (x - 9):
y - 5 = -4x + 36
Next, we rearrange the equation to isolate y:
y = -4x + 36 + 5
Simplifying further:
y = -4x + 41
Thus, the equation of the line in slope-intercept form is y = -4x + 41.