Math CentralQuandaries & Queries


Question from jenny, a parent:

write an equation in the point-slope form and the intercept form
slope=4,passing through (1,3)
slope=8,passing through (4,-1)
slope= -5,passing through (-4,-2)
slope= -2,passing through(0,-3)

Hi Jenny,

The equation of a line in "point-slope form" is given by y - y1 = m (x - x1) where m is the slope of the line and (x1, y1) is a point that the line passes through.

Using the first of your questions: slope = 4, passing through (1, 3)
m = 4
x1 = 1
y1 = 3
Therefore the point-slope form is: y - 3 = 4 (x - 1)

To convert this equation into slope-intercept form (y = mx + b) simply requires that we expand the right hand side to eliminate the brackets, and then isolate y on the left:
y - 3 = 4x - 4
y = 4x - 1
In this form we can tell that the slope of the line, m, is 4 and the y-intercept of the line, b, is -1.

Hope this helps you with the balance of your problems.

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