Straight line graph

• What is the main focus of today's lesson?

  Graphing linear equations
• Why did the instructor want students to create a table of values?


  To understand that any function can be graphed using a table of values
• How can you graph a linear equation without plotting many points?


  By using only two points
• What is the slope-intercept form of a linear equation?


  It is expressed as $y =$$mx +$$b$
• What does the variable $b$ represent in the slope-intercept form?


  The y-intercept
• How do you identify the y-intercept from the slope-intercept form?


  It is the point $(0, b)$ on the y-axis
• What is the difference between the y-intercept and the slope?


  The y-intercept is a point, while the slope is a ratio
• What is the slope defined as?


  A ratio of the change in y-values to the change in x-values
• If the slope is given as 3, how can it be expressed in fractional form?


  As $\frac{3}{1}$
• How do you find the next point using the slope?


  By moving up 3 units and over 1 unit from the y-intercept
• What does the instructor mean by "the change is positive three"?


  It means to move up three units on the y-axis
• How does the slope help in graphing a linear equation?


  It indicates how to move from one point to the next on the graph
• What is the first step in graphing a linear equation using slope-intercept form?


  Plot the y-intercept
• If the y-intercept is $(0, -5)$, where do you plot this point?


  On the y-axis at -5
• Why is it acceptable to start plotting from a negative y-intercept?


  Because the graph can start from any point on the y-axis
• What is the significance of connecting the plotted points in graphing?


  It creates the visual representation of the linear equation
• What is the importance of understanding the difference between linear, quadratic, and cubic functions?


  It helps in choosing the appropriate graphing method for each type of function
• Why might using a table of values be problematic for graphing quadratics?


  Because it may not accurately represent the shape of the graph
• What does "rise over run" refer to in the context of slope?


  It refers to the vertical change (rise) over the horizontal change (run)
• How do you determine the next point based on the slope?


  By applying the rise and run from the current point
• What is the visual representation of the graph created by connecting points?


  It shows the relationship defined by the linear equation
• We can use the formula y = mx + c to write down an equation of a straight line.
• A straight-line graph has an equation of the form y = mx + c, where m is the gradient and c is the vertical intercept.
• If we know two points on a straight line, we can find its equation.