The slope, m, compares the change in y-values to the change in x-values. Use the points (2, 4) and (6, 6) to determine the slope.
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1 LESSON Relating Slope and -intercept to Linear Equations UNDERSTAND The slope of a line is the ratio of the line s vertical change, called the rise, to its horizontal change, called the run. You can find the slope of a line from an two points on the line. You can confirm this b comparing the slopes of two segments on a line The slope, m, compares the change in -values to the change in -values. Use the points (, ) and (, ) to determine the slope. m change in change in m, so the slope of the line from (, ) to (, ) is. Use the points (, ) and (, ) to determine the slope. m change in change in m, so the slope of the line from (, ) to (, ) is. Compare the slopes. The slope calculated from the first line segment is the same as the slope calculated from the second line segment. It does not matter which points on a line are used to determine slope. Duplicating an part of this book is prohibited b law. Domain : Epressions and Equations
2 Connect You can determine the equation of an line passing through the origin. Determine the slope for the following line, which passes through the origin. Then use it to write the equation of the line Use the given changes in and to determine the slope, m. The change in is labeled on the graph. The change in is labeled on the graph. m change in values change in values _ Use two points on the graph to find the slope, m. Solve the equation for. m _ m() () m Multipl both sides b. Cancel the s on the right side. The equation is m. This is the equation of an line that passes through the origin. Duplicating an part of this book is prohibited b law. The line passes through points (0, 0) and (, 9). m The slope of the line that passes through (0, 0) and (, 9) is. Using the equation m, the equation of this line is. DISCUSS If ou know that a line passes through the origin and ou know the coordinates of another point on the line, how can ou use the equation m to determine the slope? Lesson : Relating Slope and -intercept to Linear Equations
3 EXAMPLE What is the equation of the line graphed below? 0 Find ordered pairs from the graph. Determine the slope, m, of the line. (, ), (, 0), (0, ), (, ) Determine if is the equation of the line. Use an two points, such as (, 0) and (, ). m 0 () The slope of the line is. Compare the graph of with the given graph. 0 The given graph intersects the -ais at. The graph of intersects the -ais at 0. The given graph has points that are units up from the points for. is not the equation of the line. CHECK The slope-intercept form for a linear equation is m b, where m is the slope of the line and b is the -intercept. Adding units to each point of results in the equation, where the slope is and the -intercept is. The equation of the line is. Substitute,, 0, and for in the equation. Do the resulting -values match those in the ordered pairs? Duplicating an part of this book is prohibited b law. Domain : Epressions and Equations
4 read Problem Solving A coordinate graph has points at (, ), (, ), and (, ). Can the points lie on the same line on the graph? plan Ever line segment of a line has the same. Therefore, if the the line. If the solve of the segment between (, ) and (, ) is the same as of the segment between (, ) and (, ), the points lie on the same is not the same, then the points do not lie on the same line. Find the of the segment between (, ) and (, ). Find the of the segment between (, ) and (, ). Duplicating an part of this book is prohibited b law. Therefore, the points (, ), (, ), and (, ) [do / do not] lie on the same line. Circle one check Use a coordinate graph to check the answer. Plot the given points on the graph. The points (, ), (, ), and (, ) [do / do not] lie on the same line. Does this match our answer? The points (, ), (, ), and (, ) [do / do not] lie on the same line Lesson : Relating Slope and -intercept to Linear Equations 9
5 Practice Determine the slope and -intercept from each graph HINT If a graph passes through the origin, what will its -intercept be? Determine the slope and -intercept from each equation Write an equation from each -intercept and slope. 9. equation: 0. equation: Duplicating an part of this book is prohibited b law. 0 Domain : Epressions and Equations
6 Determine the slope and -intercept from each table of coordinates. Then write an equation and eplain how ou found the information to determine the equation Equation: Equation: Choose the best answer.. Which ordered pair represents a point that would lie on the graph of 0? A. (, 0) B. (, ) C. (, ) D. (, 0). Which is the equation of a line that intersects the -ais at and has a slope of? A. B. C. D. Solve. Duplicating an part of this book is prohibited b law.. CONSTRUCT Write the equation of a line that passes through points (, ) and (, ). Describe the steps ou took to form the equation.. EXPLAIN In our own words, eplain how ou could tell whether (, ), (, 0), and (, ) lie in the same line. Lesson : Relating Slope and -intercept to Linear Equations
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