The distance from home is 0 miles and 0 minutes have passed. ( 0, 0 ) ( 0, 0 ) is the x x- and y y-intercept and represents Juan at home before his bike ride.Create an interpretation of this graph (i.e., make up a story that goes with it).Y - intercept is ( 0, 3 ) y - intercept is ( 0, 3 ). Step 5: Write the slope-intercept form of the equation of the line. When an equation of a line is not given in slope-intercept form, our first step will be to solve the equation for y y.Y - intercept is ( 0, − 2 ) y - intercept is ( 0, − 2 ) Step 1: Write the slope-intercept form of the equation of the line. We compare our equation to the slope-intercept form of the equation.Identify the slope and y y-intercept of the line from the equation: Let’s review how the rise and run relate to the coordinates of the two points by taking another look at the slope of the line between the points ( 2, 3 )Figure 5.80.įinding the Slope and y y-Intercept of a Line If we had more than two points, (if we were finding more than one slope), we could use ( x 3 x 3, y 3 y 3), ( x 4 x 4, y 4 y 4), and so on. For example, ( x 1 x 1, y 1 y 1) would be said aloud as “ x x sub 1, y y sub 1” and ( x 2 x 2, y 2 y 2) read “ x x sub 2, y y sub 2.” The “sub” is a short way of saying “subscript.” We will use ( x 1 x 1, y 1 y 1) to identify the first point and ( x 2 x 2, y 2 y 2) to identify the second point in our slope equation. How can the same symbol ( x x, y y) be used to represent two different points? Mathematicians use subscripts to distinguish such points. But when we work with slopes, we use two points. We have seen that an ordered pair ( x x, y y) gives the coordinates of a point. First, we need to introduce some algebraic notation. We could plot the points on grid paper, then count out the rise and the run, but there is a way to find the slope without graphing. Sometimes we will need to find the slope of a line between two points when we don’t have a graph to measure the rise and the run.
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