Question - Graphing a Linear Equation in Point-Slope Form
Solution:
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.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com