Math: Linear Equations (Middle School) Worksheet

Question 1

Solve for x: x + 7 = 19.

Accepted Answer

x = 12 because 12 + 7 = 19.

Question 2

Solve for y: 4y = 36.

Accepted Answer

y = 9 because 4 times 9 equals 36.

Question 3

Solve for n: n/5 = 8.

Accepted Answer

n = 40 because 40 divided by 5 equals 8.

Question 4

Solve for a: 3a + 5 = 20.

Accepted Answer

a = 5 because 3 times 5 plus 5 equals 20.

Question 5

Solve for m: 2m - 9 = 15.

Accepted Answer

m = 12 because 2 times 12 minus 9 equals 15.

Question 6

Solve for p: 5p + 4 = 2p + 19.

Accepted Answer

p = 5 because 5 times 5 plus 4 equals 29, and 2 times 5 plus 19 also equals 29.

Question 7

Solve for x: 6(x - 2) = 30.

Accepted Answer

x = 7 because 6 times the quantity 7 minus 2 equals 30.

Question 8

Solve for t: 4t + 3 = 2(t + 9).

Accepted Answer

t = 7.5 because 4 times 7.5 plus 3 equals 33, and 2 times the quantity 7.5 plus 9 also equals 33.

Question 9

A line has the equation y = 2x + 1. Complete the table for x = 0, 1, 2, and 3.

Accepted Answer

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.

Question 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.

Accepted Answer

The equation is y = 3x + 4 because the slope is 3 and the y-intercept is 4.

Question 11

Find the slope of the line that passes through the points (2, 5) and (6, 13).

Accepted Answer

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.

Question 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.

Accepted Answer

The equation is y = 2x + 3 because the cost increases by $2 for each mile and starts at $3.

Question 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.

Accepted Answer

The equation is y = 5x + 12. After 8 weeks, she will have y = 5(8) + 12 = 52 dollars.

Question 14

A line is shown passing through the points (0, -2) and (4, 6). Write the equation of the line in slope-intercept form.

Accepted Answer

The equation is y = 2x - 2 because the slope is 2 and the line crosses the y-axis at -2.

Question 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.

Accepted Answer

The equation is y = 4x + 3 because y increases by 4 each time x increases by 1, and substituting x = 1 gives 7.

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Math: Linear Equations (Middle School)

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