Graphing Linear and Systems of Equations Worksheet

Question 1

Graph the equation y = 2x + 1. State the slope and the y-intercept.

Accepted Answer

The line has slope 2 and y-intercept 1. It crosses the y-axis at (0, 1) and rises 2 units for every 1 unit it moves to the right.

Question 2

Graph the equation y = -3x + 4. Describe how the line moves from left to right.

Accepted Answer

The line crosses the y-axis at (0, 4) and has slope -3. From left to right, the line goes downward 3 units for every 1 unit it moves to the right.

Question 3

Write the equation of a line with slope 1/2 and y-intercept -3. Then describe how you would graph it.

Accepted Answer

The equation is y = (1/2)x - 3. To graph it, plot the y-intercept at (0, -3), then move up 1 unit and right 2 units to find another point, and draw the line through the points.

Question 4

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

Accepted Answer

The slope is 2 because (13 - 5) / (6 - 2) = 8 / 4 = 2.

Question 5

Find the slope of the line that passes through the points (-1, 4) and (3, -8).

Accepted Answer

The slope is -3 because (-8 - 4) / (3 - (-1)) = -12 / 4 = -3.

Question 6

Determine whether the line through the points (0, 2) and (4, 2) is increasing, decreasing, horizontal, or vertical. Explain.

Accepted Answer

The line is horizontal because the y-value stays 2 for both points. A horizontal line has slope 0.

Question 7

Graph the equation x = -5. Describe the line and state whether its slope is defined.

Accepted Answer

The graph is a vertical line that passes through all points with x = -5. Its slope is undefined because the run is 0.

Question 8

Rewrite 3x + y = 7 in slope-intercept form. Then state the slope and y-intercept.

Accepted Answer

The equation in slope-intercept form is y = -3x + 7. The slope is -3 and the y-intercept is 7.

Question 9

Rewrite 2x - 4y = 12 in slope-intercept form. Then identify the slope and y-intercept.

Accepted Answer

The equation in slope-intercept form is y = (1/2)x - 3. The slope is 1/2 and the y-intercept is -3.

Question 10

Solve the system by graphing: y = x + 2 and y = -x + 4. State the solution as an ordered pair.

Accepted Answer

The solution is (1, 3) because the two lines intersect at the point where x = 1 and y = 3.

Question 11

Solve the system by graphing: y = 2x - 1 and y = 2x + 3. Explain what the graph shows.

Accepted Answer

This system has no solution because both lines have the same slope of 2 but different y-intercepts. The lines are parallel and never intersect.

Question 12

Solve the system by graphing: y = -4x + 5 and y = -4x + 5. Explain your answer.

Accepted Answer

This system has infinitely many solutions because both equations represent the same line. Every point on the line satisfies both equations.

Question 13

A gym charges a one-time sign-up fee of 20 dollars and 15 dollars per month. Write a linear equation where x is the number of months and y is the total cost. Then state the slope and y-intercept.

Accepted Answer

The equation is y = 15x + 20. The slope is 15 because the cost increases by 15 dollars each month, and the y-intercept is 20 because the starting fee is 20 dollars.

Question 14

A line has y-intercept 6 and passes through the point (2, 2). Find its slope and write the equation in slope-intercept form.

Accepted Answer

The y-intercept gives the point (0, 6). The slope is (2 - 6) / (2 - 0) = -4 / 2 = -2, so the equation is y = -2x + 6.

Question 15

Compare the lines y = 3x - 2 and y = -(1/3)x - 2. Tell whether they intersect, and if so, find the point of intersection.

Accepted Answer

The lines intersect because they have different slopes. Since both have the same y-intercept of -2, they intersect at (0, -2).

Graphing Linear and Systems of Equations

Graphing Linear and Systems of Equations

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