Math: Linear Equations (Middle School)
Solving, graphing, and writing linear equations
Math: Linear Equations (Middle School)
Solving, graphing, and writing linear equations
Math - Grade 6-8
- 1
Solve for x: x + 7 = 19.
Use the inverse operation of addition.
x = 12 because 12 + 7 = 19. - 2
Solve for y: 4y = 36.
y = 9 because 4 times 9 equals 36. - 3
Solve for n: n/5 = 8.
Use the inverse operation of division.
n = 40 because 40 divided by 5 equals 8. - 4
Solve for a: 3a + 5 = 20.
Undo the addition first, then undo the multiplication.
a = 5 because 3 times 5 plus 5 equals 20. - 5
Solve for m: 2m - 9 = 15.
m = 12 because 2 times 12 minus 9 equals 15. - 6
Solve for p: 5p + 4 = 2p + 19.
Move the variable terms to one side and the number terms to the other side.
p = 5 because 5 times 5 plus 4 equals 29, and 2 times 5 plus 19 also equals 29. - 7
Solve for x: 6(x - 2) = 30.
You can divide both sides by 6 first or use the distributive property.
x = 7 because 6 times the quantity 7 minus 2 equals 30. - 8
Solve for t: 4t + 3 = 2(t + 9).
t = 7.5 because 4 times 7.5 plus 3 equals 33, and 2 times the quantity 7.5 plus 9 also equals 33. - 9
A line has the equation y = 2x + 1. Complete the table for x = 0, 1, 2, and 3.
Substitute each x-value into the equation.
The completed table is (0, 1), (1, 3), (2, 5), and (3, 7). Each y-value is found by multiplying x by 2 and adding 1. - 10
The graph of a line crosses the y-axis at 4 and rises 3 units for every 1 unit it moves to the right. Write the equation of the line in the form y = mx + b.
In y = mx + b, m is the slope and b is the y-intercept.
The equation is y = 3x + 4 because the slope is 3 and the y-intercept is 4. - 11
Find the slope of the line that passes through the points (2, 5) and (6, 13).
The slope is 2 because the change in y is 13 - 5 = 8 and the change in x is 6 - 2 = 4, so 8 divided by 4 equals 2. - 12
Write an equation for this situation: A taxi charges a starting fee of $3 plus $2 for each mile. Let x be the number of miles and y be the total cost in dollars.
The starting fee is the y-intercept, and the cost per mile is the slope.
The equation is y = 2x + 3 because the cost increases by $2 for each mile and starts at $3. - 13
A student saves $5 each week. She already has $12 saved. Write an equation for the total amount of money y after x weeks. Then find the amount after 8 weeks.
The equation is y = 5x + 12. After 8 weeks, she will have y = 5(8) + 12 = 52 dollars. - 14
A line is shown passing through the points (0, -2) and (4, 6). Write the equation of the line in slope-intercept form.
Use the point (0, -2) to find the y-intercept.
The equation is y = 2x - 2 because the slope is 2 and the line crosses the y-axis at -2. - 15
The table shows a linear relationship: when x is 1, y is 7; when x is 2, y is 11; when x is 3, y is 15; when x is 4, y is 19. Write an equation that represents the relationship.
First find the change in y for each increase of 1 in x.
The equation is y = 4x + 3 because y increases by 4 each time x increases by 1, and substituting x = 1 gives 7.