Question - Graphing a Line from Point-Slope Form Equation
Solution:
To graph the line given by the equation $$ y - 2 = \frac{-2}{5}(x - 4) $$, you can follow these steps:1. Recognize the equation form:The equation is in point-slope form, $$ y - y_1 = m(x - x_1) $$, where $$ (x_1, y_1) $$ is a point on the line and $$ m $$ is the slope of the line.2. Identify the slope and a point:From the given equation, the slope ($$ m $$) is $$ -\frac{2}{5} $$ and the point ($$ x_1, y_1 $$) is (4, 2).3. Plot the given point:Start by plotting the point (4, 2) on the coordinate plane. This is a point through which the line will pass.4. Use the slope to find another point:The slope $$ -\frac{2}{5} $$ means that for every 5 units you move to the right (in the positive x-direction), you move 2 units down (in the negative y-direction) because the slope is negative. You could also move 5 units to the left (negative x-direction) and 2 units up (positive y-direction) to find another point.5. Plot the second point:For example, starting at point (4, 2) and moving 5 units to the right, you reach the point (9, 0). Plot this point on the coordinate plane.6. Draw the line:Once you have these two points plotted, you can use a ruler to draw a straight line through them, extending it across the coordinate plane. This line represents all the points that satisfy the equation.Here's a rough step-by-step description of plotting the points and drawing the line:- Place a dot at (4, 2).- From (4, 2), move 5 units to the right to get to (9, 2).- From (9, 2), move 2 units down to get to (9, 0).- Place a dot at (9, 0).- Connect the two dots with a straight line.- Extend the line through and beyond both points to indicate that it continues infinitely in both directions.If you're graphing this by hand or using a graphing tool, make sure to label your axes and scale appropriately to accurately depict the slope and points.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com