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We need to find the equation of the line that has slope m = 6 and passes throught the point (2, 5)
We use the information on the general equation of a line in slope-point form:
y - y0 = m (x - x0)
where (x0, y0) are the coordinates of the desired point ) in our case the point (2, 5)), and m is the slope.
So we re-write the general expression as:
y - 5 = 6 (x - 2)
This is the equation of the line in Point-Slope form
If we want the equation in Slope-Intercept form, we use distributive property :
y - 5 = 6 x - 12
now add 5 to both sides to isolate y on the left
y = 6 x - 12 + 5
y = 6 x - 7
This is the equation of the line in slope-intercept form.
Please notice the difference between one form and the other.
It seems your teacher wants the Point-Slope form for this problem on the list.