Example Question - graphing linear equation
Here are examples of questions we've helped users solve.
Graphing a Linear Equation in Point-Slope Form
The equation provided in the image is a linear equation in point-slope form, which is \( y - y_1 = m(x - x_1) \), where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope of the line. The given equation is: \[ y - 5 = -\frac{8}{3}(x - 6) \] From this equation, we can identify the slope \( m = -\frac{8}{3} \) and a point on the line \( (x_1, y_1) = (6, 5) \). To graph this line, follow these steps: 1. Plot the point \( (6, 5) \) on a coordinate plane. 2. Use the slope to find additional points. The slope \( -\frac{8}{3} \) means that for every 3 units you move to the right (positive direction along the x-axis), you move 8 units down (negative direction along the y-axis). 3. From \( (6, 5) \), move 3 units to the right to \( (9, 5) \) and then 8 units down to \( (9, -3) \). Plot this second point. 4. Draw a straight line through the two points to extend it across the graph. Now you have graphed the line based on the provided linear equation.
Graphing a Linear Equation
To solve the equation and complete the ordered pairs, you need to plug the x-values from each ordered pair into the equation y = -x/5 + 2 and solve for y. The equation is linear, which means you will be graphing a straight line. You only need two points to define a straight line, but let's find the y-values for all the given x-values: 1. For the ordered pair (-5, _), plug in x = -5: y = -(-5)/5 + 2 y = 5/5 + 2 y = 1 + 2 y = 3 So, the complete ordered pair is (-5, 3). 2. For the ordered pair (0, _), plug in x = 0: y = -(0)/5 + 2 y = 0 + 2 y = 2 So, the complete ordered pair is (0, 2). 3. For the ordered pair (5, _), plug in x = 5: y = -(5)/5 + 2 y = -1 + 2 y = 1 So, the complete ordered pair is (5, 1). To graph these points, you just need to put these coordinates on a graph and draw a straight line through them. Using (-5, 3) and (5, 1), you can draw the graph as follows: - Plot the point (-5, 3) on the graph. - Plot the point (5, 1) on the graph. - Draw a straight line that passes through both points, extending it on both ends. This line is the graphical representation of the solution set for the equation y = -x/5 + 2.
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