Writing+Linear+Functions-Target+B-Equivalent?-Guided+Learning

Writing Linear Functions Target B: Convert Linear Functions
Whom do you agree with and why? ||
 * [[image:Discuss this.png width="173" height="97"]] || Tina claims that determining the x-intercept for a linear function is easier in standard form. Justin disagrees with Tina. He thinks that slope intercept form is easier to determine the x-intercept.

Why would you need to know three different ways to write a linear equation? Seems silly, right? The reason is that each form provides different pieces of information relating to the graph of the function! Slope-intercept form provides the slope and the y-intercept of the graph of a function. Point-slope form provides information such as the slope and a point that the graph of the line passes through. Finally, standard form can easily provide us with the location of the x-intercept and the y-intercept. There is a lot of information that can be learned about the graph of a function from the three different forms for writing a linear equation. Look at the graph below: The equation of the line written in slope-intercept form is y = -3/4x - 3. Looking at the graph, you can see that the slope of the line is -3/4 and that the y-intercept is (0, -3). When the equation of the same line is written in point slope form, y - 3 = -3/4(x + 8), you can see that the graph of the line passes through the point (-8, 3), and that the slope is still -3/4. When the equation of the line is written in standard form, 3x + 4y = -12, you can pull the intercepts from the equation to see that the x-intercept would be (-4, 0), and the y-intercept would be (0, -3), which is where the line crosses the differnt axes in the graph (to recall how to find the intercepts from an equation in standard form, go to Graphing Linear Functions Target D Guided Learning- Standard Form). All of these three equations are equivalent to one another because they all represent the equation of the same line!

What happens if there is no graph? Given the linear equation y + 5 = 2(x - 1), how can you determine where the graph of the line would cross the y-axis? You would need to convert the equation into slope-intercept form or substitute in zero for x so that you could find the y-intercept!

Watch the videos below to learn how to convert from one form to another to come up with equivalent equations that all represent the graph of the same line.

Converting from Slope-Intercept Form to Write an Equivalent Equation in Standard Form media type="custom" key="26300642"

Converting from Point-Slope Form to Write an Equivalent Equation in Slope-Intercept Form or Standard Form media type="custom" key="26300706"

Recall how to convert from Standard Form to Slope-Intercept (Function) Form by going to Equations and Inequalities-Target B-Guided Learning


 * Writing Linear Functions-Target B-Equivalent-Quick Check:**

Write an equivalent equation in the specified form. math 1)\ \ y-4=\dfrac{2}{3}(x + 6)\ \ \text{in standard form} math math 2)\ \ 5x-2y=10\ \ \text{in slope-intercept form} math

Writing Linear Functions-Target B-Equivalent-Quick Check Solutions