The complete factoring is:
Remind them that in order to write the equation of a line in slope-intercept form you need to know two things: Their task is to find both of those values. Just as in the warm-up, students will approach the problem in different ways.
Some students will plot the point and use the slope to work backwards. Others will determine the y-intercept by subtracting 0. Others may even determine that since they have to go back 4 units on the x-axis they must go down 2 units on the y-axis. When students share out their answers, encourage the generation of different ideas.
Try to scaffold answers in a strategic way. For example, have a group that knew a change of 4 in the x-direction would result in a change of 2 in the y-direction could build on a group that subtracted 0.
This strategic scaffolding of answers will help all members of the class understand the concept at a deeper level. Refer back to the idea that a line is really a collection of points that all make the equation of the line true.
Give students a minute to think and then guide them towards the idea of plugging in the point 4, 7 to the equation to show that it makes a true statement. Slide 2 In the second slide, we are going to work backwards from this understanding. Start by making a connection back to the previous question showing that the slope and the x-value will result in a certain y-value so mx would be 0.
If we move 4 in the x-direction we move 2 in the y-direction but we want the y-value to be 7. Students should be able to see that the y-value is 5. They should be starting to make a connection based on the work they did in the first part of the problem with no previous instruction.
Students can now picture in a more concrete way what this abstract approach represents MP2. Slide 3 This formula is almost certainly new for students.
In this form h,k is the point on the line and m is the slope. Slide 4 and 5 The next two slides offer students the opportunity to practice these two methods independently or with a partner.
In both cases, after students obtain two answers that match they should check their results graphically. This means that students should plot the point and use the slope to work towards the y-axis in order to find the y-intercept.Using this equation and knowledge of the meaning of each term in the general equation, you can easily determine the equation of a horizontal line or any other straight line.
Identify the y-intercept. For example, a horizontal line that crosses the y-axis at 2 would have a y-intercept of 2. Since the equation here is in slope-intercept form, there is a nicer way.
Since this equation is for starting with a Celsius temperature and obtaining a Fahrenheit temperature, it makes sense to let \(C\) be the horizontal axis variable and \(F\) be the vertical axis variable.
To write an equation in point-slope form, given a graph of that equation, first determine the slope by picking two points. Then pick any point on the line and write it as an ordered pair (h, k).
This form consists of a pair of equations; the first equation gives the x coordinate and the second equation gives the y coordinate of a point on the line as functions of a parameter t.
(x 1, y 1) is a known point on the line and m is the slope of the line. Write the equation in slope-intercept form. y mx b Substitute the given values for m and b. y 4x 3 A line has a slope of 2. The ordered pair 3, 1 is on the line.
Write the equation that describes each line in slope-intercept form. 1. slope 1__, 4 y-intercept 3 2. slope 5, y-intercept 0. Steps for Graphing a Linear Function (Slope-Intercept Form)! Identify and plot the y-intercept!
Use the slope to plot an additional point (Rise/Run)! Draw a line through the two points EXAMPLES EXAMPLE 5: WRITING AND GRAPHING LINEAR EQUATIONS GIVEN A Y-INTERCEPT AND A SLOPE Write an equation of a line with the given slope and y-intercept.
Then graph the equation.