Part 1.
An equation is in slope-intercept form when it matches the pattern
.. y = m·x + b . . . . . . . for some constants m and b and some variables y and x
The slope is given by the constant "m". The y-intercept is given by the constant "b".
7. slope = 3, y-intercept = 1
15. slope = [tex] \frac{1}{4}[/tex], y-intercept = [tex] -\frac{1}{3}[/tex]
Part 2.
Put the given numbers in the pattern for slope-intercept form.
20. y = -0.5x +1.5
Part 3.
The y-intercept (b) is the y-coordinate where the line crosses the y-axis. The slope (m) is found by identifying two places where the line crosses grid points, then forming the ratio (vertical distance between grid crossings)/(horizontal distance between grid crossings). If the line goes up to the right, the ratio and slope are positive. If the line goes down to the right, they are negative.
23. The line crosses the y-axis at y=-3. It also crosses grid point (1, -1), which is 2 units up and 1 unit over from the y-intercept (0, -3). Hence the slope is m = 2/1 = 2. The equation of the line is
.. y = 2x -3
Part 4.
There is another pattern that is useful when two points are given. That is the "two-point form" of the equation for a line.
.. y = (y2 -y1)/(x2 -x1)*(x -x1) +y1 . . . . . . . for points (x1, y1) and (x2, y2)
This can be simplified to give the desired point-slope form after the numbers are filled in.
29. (x1, y1) = (-2, 4); (x2, y2) = (3, -1). The line can be written as
.. y = (-1 -4)/(3 -(-2))*(x -(-2)) +4 . . . . the 2-point form with numbers filled in
.. y = (-5/5)*(x +2) +4 . . . . . . . . . . . . simplified a bit
.. y = -(x +2) +4 . . . . . . . . . . . . . . . .. simplified more
.. y = -x -2 +4 . . . . . . . . . . . . . . . . . . parentheses eliminated
.. y = -x +2 . . . . . . . . . . . the desired equation
