Algebra 1 Semester 1 Lesson 5: Linear Functions and Models
Finding Slope:
Another name for slope is “Rate of Change.”
To find slope on a graph, you find 2 points that are exactly on an intersection, and then measure
the “rise” or amount of units up or down, and the “run,” the amount of units left or right. This is
the distance from one point to another.
Using the formula (rise)/(run) you can figure out the slope.
To find the slope using 2 points, you use the formula: (y2-y1)/(x2-x1).
Examples:
1: (6, 5) and (-4, 1)
2: (-13, 7) and (0, 8)
3: (-20, 18) and (14, 6)
4: (19, -17) and (12, 4)
5: (-1, 7) and (-14, 3)
6: (3, -4) and (-12, 11)
7: (15, -14) and (-2, 16)
Correct Answers:
1: 2/5
2: 1/13
3: -6/17
4: 3
5: 4/13
6: -1
7: -30/17
Explanation:
To find the slopes using two points, you need to use the formula: (y2-y1)/(x2-x1). The x of the
first point (first number) is x1, the y of the first point (second number) is y1, the x of the second
point (first number of second parenthesis) is x2, and the y of the second point (second number
of second parenthesis) is y2. Once you understand this, you can subtract the first y from the
second y, and put it above the second x minus the first y. Keep in mind that if the x1 or y1 is
negative, you will add the number instead of subtracting.
Special Cases:
If, in your slope formula, the top number is equal to zero, that makes a “zero slope” or a
horizontal line. If the bottom number is 0, that makes an “undefined slope” or a vertical line.
Examples:
1: (5, 6) and (-4, 6)
2: (3, -4) and (3, 8)
Finding Slope:
Another name for slope is “Rate of Change.”
To find slope on a graph, you find 2 points that are exactly on an intersection, and then measure
the “rise” or amount of units up or down, and the “run,” the amount of units left or right. This is
the distance from one point to another.
Using the formula (rise)/(run) you can figure out the slope.
To find the slope using 2 points, you use the formula: (y2-y1)/(x2-x1).
Examples:
1: (6, 5) and (-4, 1)
2: (-13, 7) and (0, 8)
3: (-20, 18) and (14, 6)
4: (19, -17) and (12, 4)
5: (-1, 7) and (-14, 3)
6: (3, -4) and (-12, 11)
7: (15, -14) and (-2, 16)
Correct Answers:
1: 2/5
2: 1/13
3: -6/17
4: 3
5: 4/13
6: -1
7: -30/17
Explanation:
To find the slopes using two points, you need to use the formula: (y2-y1)/(x2-x1). The x of the
first point (first number) is x1, the y of the first point (second number) is y1, the x of the second
point (first number of second parenthesis) is x2, and the y of the second point (second number
of second parenthesis) is y2. Once you understand this, you can subtract the first y from the
second y, and put it above the second x minus the first y. Keep in mind that if the x1 or y1 is
negative, you will add the number instead of subtracting.
Special Cases:
If, in your slope formula, the top number is equal to zero, that makes a “zero slope” or a
horizontal line. If the bottom number is 0, that makes an “undefined slope” or a vertical line.
Examples:
1: (5, 6) and (-4, 6)
2: (3, -4) and (3, 8)
