1.1 Integers and Rational Numbers

11.1. Writing Linear Equations in Slope-Intercept Form www.ck12.orgStep 5: Rewrite y = mx + b, substituting the slope for m and the y−intercept for b.y = − 2 5 x + 165Example 6: Write the equation for a line containing the points (-4, 1) and (-2, 3).Solution:1. Start with the slopeintercept form of the line y = mx + b.2. Find the slope of the line. m = y 2−y 1x 2 −x 1=3−1−2−(−4) = 2 2 = 13. Substitute the value of slope for m : y = (1)x + b4. Substitute the coordinate (-2, 3) into the equation for the variables x and y : 3 = −2 + b ⇒ b = 55. Rewrite the equation, substituting the slope for m and the y−intercept for b. y = x + 5Writing a Function in Slope-Intercept FormRemember that a linear function has the form f (x) = mx + b. Here f (x) represents the y values of the equation orthe graph. So y = f (x) and they are often used interchangeably. Using the functional notation in an equation oftenprovides you with more information.For instance, the expression f (x) = mx + b shows clearly that x is the independent variable because you substitutevalues of x into the function and perform a series of operations on the value of x in order to calculate the values ofthe dependent variable, y.In this case when you substitute x into the function, the function tells you to multiply it by m and then add b to theresult. This process generates all the values of y you need.Example 7: Consider the function f (x) = 3x − 4. Find f (2), f (0), and f (−1).Solution: Each number in parentheses is a value of x that you need to substitute into the equation of the function.f (2) = 2; f (0) = −4; and f (−1) = −7Function notation tells you much more than the value of the independent variable. It also indicates a point on thegraph. For example, in the above example, f (−1) = −7. This means the ordered pair (-1, -7) is a solution tof (x) = 3x − 4 and appears on the graphed line. You can use this information to write an equation for a function.Example 8: Write an equation for a line with m = 3.5 and f (−2) = 1.Solution: You know the slope and you know a point on the graph (-2, 1). Using the methods presented in this lesson,write the equation for the line.Begin with slope-intercept form212