<transcript><audio_38>line and let's pause a moment and see what we've gotten if y equals C is a horizontal line and X equal C is a vertical line then what happens when we have an equation that involves both x and y like 5x plus 3y equals 15 as</transcript><caption><image_39>The image is a screenshot of a slide from a presentation on linear equations. The slide has a title "Linear Equations" at the top and a subtitle "Theorem (Horizontal Lines)". Below the title, there are two options - Theorem (Vertical Lines) and the text "The graph of y = c, where is a any constant, is a horizontal line". The text is written in black font on a white background.</caption><transcript><audio_40>before we'll find some points but before we proceed we'll throw down a useful definition and a theorem the standard equation of a line is ax plus B y equals</transcript><transcript><audio_41>C where a B and C are real numbers well actually I'm putting Descartes before the course because we should actually point out that the graph of ax</transcript><transcript><audio_42>so let's take a look at the graph of 3x plus 5y equals 15 so our definition says that we have the standard equation for a line and the theorem says that when we graph this we will actually get a</transcript><caption><image_43>The image is a screenshot of a math worksheet with a title "Definition (Standard Equation of a Line)". The worksheet is divided into two sections. The top section has a green header with the title "Example" and a white background. Below the header, there is a text field with the text "The standard equation of a line" and "where a.e.g. are real numbers". The text field is blank, indicating that the user is in the process of filling in the equation.</caption><transcript><audio_44>straight line so from geometry we know that we only need two points to graph a line so let's find two points that satisfy this equation since we get to pick our X or Y values we want to pick the hardest possible value so that</transcript><transcript><audio_45>people will marvel at our awesomeness or we might actually want to pick the easiest values that we can work with so we like 0 if x equals 0 then substituting that into our formula gives us an equation that we can solve for y</transcript><transcript><audio_46>why equals five so zero five is a point while we could pick a different value for X and solve for y we might find it a little bit easier to let y equal zero so</transcript><caption><image_47>The image is a graph that shows the relationship between two variables. The x-axis of the graph is labeled with the value "0.5" and the y-axis is labeled as "x = 0.5". Below the graph, there is a line graph with a point on the graph. On the right side of the image, there are two equations written in black text. The equation on the left side reads "Since we get to pick our x or y values, we want to pick the equation values that we can work with." The equation is written in the form of a line that starts at the top and ends at the bottom. The graph is plotted on a white background.</caption><transcript><audio_48>we'll let y equal zero and substitute that value into our equation and then and if we do that we find that three</transcript><transcript><audio_49>zero is also a point on the graph and because we know that this graph will produce a straight line will draw the straight line running between these two</transcript> line and let's pause a moment and see what we've gotten if y equals C is a horizontal line and X equal C is a vertical line then what happens when we have an equation that involves both x and y like 5x plus 3y equals 15 as before we'll find some points but before we proceed we'll throw down a useful definition and a theorem the standard equation of a line is ax plus B y equals C where a B and C are real numbers well actually I'm putting Descartes before the course because we should actually point out that the graph of ax so let's take a look at the graph of 3x plus 5y equals 15 so our definition says that we have the standard equation for a line and the theorem says that when we graph this we will actually get a straight line so from geometry we know that we only need two points to graph a line so let's find two points that satisfy this equation since we get to pick our X or Y values we want to pick the hardest possible value so that people will marvel at our awesomeness or we might actually want to pick the easiest values that we can work with so we like 0 if x equals 0 then substituting that into our formula gives us an equation that we can solve for y why equals five so zero five is a point while we could pick a different value for X and solve for y we might find it a little bit easier to let y equal zero so we'll let y equal zero and substitute that value into our equation and then and if we do that we find that three zero is also a point on the graph and because we know that this graph will produce a straight line will draw the straight line running between these two
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