Example Question - slope and point
Here are examples of questions we've helped users solve.
Finding the Equation of a Line Given Slope and Point
<p>The point-slope form of a line's equation is \( y - y_1 = m(x - x_1) \) where \( m \) is the slope and \( (x_1, y_1) \) is a point on the line.</p> <p>For the given slope \( m = 2 \) and point \( (1, 3) \), we have:</p> <p>\( y - 3 = 2(x - 1) \)</p> <p>\( y - 3 = 2x - 2 \)</p> <p>\( y = 2x + 1 \)</p>
Finding the Equation of a Line Given Slope and a Point
Given slope, \( m = 2 \), and a point, \( (1,3) \), use the point-slope form of the equation of a line: \( y - y_1 = m(x - x_1) \). Substitute \( m = 2 \), \( x_1 = 1 \), and \( y_1 = 3 \) into the equation: \( y - 3 = 2(x - 1) \) Now, simplify and put it in slope-intercept form, \( y = mx + b \): \( y - 3 = 2x - 2 \) \( y = 2x + 1 \)
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.
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