1. Given the line with the equation :
a) Find at least three ordered pairs that satisfy the equation.
b) Find the slope of the line.
c) Graph the line
2. Given the line with equation :
a) Write the equation in slope-intercept form.
b) State the slope of the line.
c) State the y-intercept of the line as an ordered pair.
d) Use the slope-intercept form to graph the line.
This makes no sense without an equation.
1. To find the ordered pairs that satisfy the equation of the line, we need to plug in different values for the variables and solve for the other variable.
a) For example, if the equation of the line is y = mx + b, where m is the slope and b is the y-intercept, we can choose different x-values and solve for y. Let's say we choose x = 0, 1, and 2:
- For x = 0, the equation becomes y = m(0) + b = b. So, one ordered pair is (0, b).
- For x = 1, the equation becomes y = m(1) + b = m + b. So, another ordered pair is (1, m + b).
- For x = 2, the equation becomes y = m(2) + b = 2m + b. So, one more ordered pair is (2, 2m + b).
These are just three examples, and you can pick any other values for x to find more ordered pairs that satisfy the equation.
b) The slope of the line can be determined by analyzing the coefficient of x in the equation. For example, if the equation of the line is y = 2x + 3, the slope is 2. If the equation is y = -3x + 5, the slope is -3. So, the slope is the number in front of x in the equation.
c) To graph the line, you can plot the ordered pairs you found in part (a) on a coordinate plane. Each ordered pair represents a point on the line. Connect the points using a straight line, and that will represent the line.
2. To work on the second question, we need the equation of the line. Since it is missing, I will assume the rest of the parts and explain accordingly.
a) To write the equation in slope-intercept form, we need the slope (m) and the y-intercept (b). If we have these values, we can write the equation as y = mx + b.
b) The slope of the line can be given in the equation, or it might be provided separately. If it is given, you can simply state the given slope.
c) The y-intercept of the line is the value of y when x is zero. If the line is in the slope-intercept form, then the y-intercept is the constant term b. You can state the y-intercept as an ordered pair (0, b).
d) To graph the line using the slope-intercept form, you can plot the y-intercept on the coordinate plane and then use the slope (m) to find additional points. Slope represents how the line rises or falls, so for every unit increase in x, we move vertically m units.
For example, if the slope is 2 and the y-intercept is (0, 3), you can plot (0, 3) on the coordinate plane and then move up 2 units and 1 unit to the right to find another point. Connecting these points will give you the line.