2 4 writing linear equations answer key

An equation in the slope-intercept form is written as

$$y=mx+b$$

Where m is the slope of the line and b is the y-intercept. You can use this equation to write an equation if you know the slope and the y-intercept.

Example

Find the equation of the line

Choose two points that are on the line

Calculate the slope between the two points

$$m=\frac{y_{2}\, -y_{1}}{x_{2}\, -x_{1}}=\frac{\left (-1 \right )-3}{3-\left ( -3 \right )}=\frac{-4}{6}=\frac{-2}{3}$$

We can find the b-value, the y-intercept, by looking at the graph

b = 1

We've got a value for m and a value for b. This gives us the linear function

$$y=-\frac{2}{3}x+1$$

In many cases the value of b is not as easily read. In those cases, or if you're uncertain whether the line actually crosses the y-axis in this particular point you can calculate b by solving the equation for b and then substituting x and y with one of your two points.

We can use the example above to illustrate this. We've got the two points (-3, 3) and (3, -1). From these two points we calculated the slope

$$m=-\frac{2}{3}$$

This gives us the equation

$$y=-\frac{2}{3}x+b$$

From this we can solve the equation for b

$$b=y+\frac{2}{3}x$$

And if we put in the values from our first point (-3, 3) we get

$$b=3+\frac{2}{3}\cdot \left ( -3 \right )=3+\left ( -2 \right )=1$$

If we put in this value for b in the equation we get

$$y=-\frac{2}{3}x+1$$

which is the same equation as we got when we read the y-intercept from the graph.

To summarize how to write a linear equation using the slope-interception form you

1. Identify the slope, m. This can be done by calculating the slope between two known points of the line using the slope formula.
2. Find the y-intercept. This can be done by substituting the slope and the coordinates of a point (x, y) on the line in the slope-intercept formula and then solve for b.

Once you've got both m and b you can just put them in the equation at their respective position.

Video lesson

Find the equation to the graph

Presentation on theme: "2-4 Writing Linear Equations Objective: To write an equation of a line in slope intercept form given the slope and one or two points, and to write an equation."— Presentation transcript:

1 2-4 Writing Linear Equations Objective: To write an equation of a line in slope intercept form given the slope and one or two points, and to write an equation of a line that is parallel or perpendicular to the graph of a given equation.

2 Drill #22* Write the equation of the line (in point- slope form) passing through the following points and graph the line: 1.( 2, 5 ), ( 3, 8 ) 2.( -1, 3), ( 2, 4 ) 3.( 0, 1 ), ( 3, 1 )

3 Quiz tomorrow Writing equations in point- slope and slope- intercept forms given a point and the slope (parallel or perpendicular to another line) Graphing linear equations - know how to use slope and a point to graph - know how to use two points to graph Finding the line of best fit Using the line of best fit to make predictions

4 Classwork (#22*) 4.Find the equation of the line parallel to y = ¾ x + 2 and passing through ( -2, -4) and graph the line.

5 Find the value of k (#22*) Find the value of k in the following equations if the given ordered pair is a solution: 5.5x + ky = 8 (3, -1) 6.3x + 8y = k ( 0, ½ )

6 2-5 Scatter Plots Objective: To draw scatter plots and to find and use prediction equations.

7 Scatter Plot **(25.) Definition: The graph of related data points showing the correlation among the points. Generally a line of best fit can be drawn that approximates the relationship between the points. Using the equation of the line of best fit, we can predict values.

8 Plot the following data Note: When scaling axes find the maximum and minimum value for each variable. Make sure your axes are slightly bigger than your maximum values and slightly smaller than your minimum values

9 Scatter Plot: Weak Positive Correlation

10 Line of Best-Fit ** (26.) The Best-Fit line is the line that passes close to most of the data points. It does not have to pass through any of the data points. You can use the best-fit line to make predictions about the data.

11 Equation of the line of best-fit Find two points on the line: (7, 6) and (1, 0) Find the slope: m = 1 Substitute m and find b: y = 1x + b Substitute (1, 0) or (7, 6) 0 = 1(1) + b -1 = b y = 1x - 1

12 Prediction Equation **(27.) Definition: The prediction equation can be found using two points from the line of best fit (they do not have to be data points) The prediction equation can be used to estimate the value of one of the variables given the other.

13 Slope… What does the slope mean? What are the units? The slope means that the _____________ is y - unit _____________ by _____________ inc. / dec.slope every ______________ x - unit

14 Example 2 1.Make a scatter plot of the following data. 2.Draw a line of best fit. 3.Write an equation for the line of best fit relating the rate of pay (y) to the years of experience (x) Exp9431106128 Rate$17$10 $7$6$12$20$15

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