Graphing Linear and Systems of Equations
Plot lines, identify slope, and solve systems by graphing
Graphing Linear and Systems of Equations
Plot lines, identify slope, and solve systems by graphing
Math - Grade 9-12
- 1
Graph the equation y = 2x + 1. State the slope and the y-intercept.
Use slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
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. - 2
Graph the equation y = -3x + 4. Describe how the line moves from left to right.
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. - 3
Write the equation of a line with slope 1/2 and y-intercept -3. Then describe how you would graph it.
Use the form y = mx + b.
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. - 4
Find the slope of the line that passes through the points (2, 5) and (6, 13).
The slope is 2 because (13 - 5) / (6 - 2) = 8 / 4 = 2. - 5
Find the slope of the line that passes through the points (-1, 4) and (3, -8).
Use the slope formula m = (y2 - y1) / (x2 - x1).
The slope is -3 because (-8 - 4) / (3 - (-1)) = -12 / 4 = -3. - 6
Determine whether the line through the points (0, 2) and (4, 2) is increasing, decreasing, horizontal, or vertical. Explain.
The line is horizontal because the y-value stays 2 for both points. A horizontal line has slope 0. - 7
Graph the equation x = -5. Describe the line and state whether its slope is defined.
Every point on the line has the same x-coordinate.
The graph is a vertical line that passes through all points with x = -5. Its slope is undefined because the run is 0. - 8
Rewrite 3x + y = 7 in slope-intercept form. Then state the slope and y-intercept.
The equation in slope-intercept form is y = -3x + 7. The slope is -3 and the y-intercept is 7. - 9
Rewrite 2x - 4y = 12 in slope-intercept form. Then identify the slope and y-intercept.
Solve for y by isolating the y-term first.
The equation in slope-intercept form is y = (1/2)x - 3. The slope is 1/2 and the y-intercept is -3. - 10
Solve the system by graphing: y = x + 2 and y = -x + 4. State the solution as an ordered pair.
The solution is (1, 3) because the two lines intersect at the point where x = 1 and y = 3. - 11
Solve the system by graphing: y = 2x - 1 and y = 2x + 3. Explain what the graph shows.
Compare the slopes and y-intercepts of the two equations.
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. - 12
Solve the system by graphing: y = -4x + 5 and y = -4x + 5. Explain your answer.
This system has infinitely many solutions because both equations represent the same line. Every point on the line satisfies both equations. - 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.
The starting amount is the y-intercept and the monthly change is the slope.
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. - 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.
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. - 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.
Check whether the equations share the same y-intercept.
The lines intersect because they have different slopes. Since both have the same y-intercept of -2, they intersect at (0, -2).