Some students are inherently hands-on learners. One way to approach teaching the slope and y-intercept is to gather the students in a large room or in an open area outside where you have marked out a grid with colored tape or nontoxic paint. Use a different color to mark the x and y intercepts. Arrange the students in a line and then move each student slightly to make lines that are more or less steep. Use four or five students to make a line and then ask the other students to determine where the line meets the y-intercept.
Many students engage more with mathematical concepts when they mirror a real life situation. Show a PowerPoint slide or other visual that depicts a ski slope or a road with a sharp grade. Highlight a tree or building along the slope or road. Then, superimpose a graph over the slide or visual. Ask the students to pretend that they are a skier or snowboarder, or that they are driving their car down the road. Ask them to find the what point on the graph when they will reach the tree or building.
Many students are more engaged with math when you pair it with technology. You can demonstrate how slope and y-intercept works by having the students enter the data for a line into a graphing calculator. Ask them to follow along as you change the data slightly, which will affect the slope and the y-intercept. Talk to them about what they are seeing on their calculators. Then, have them try to draw a line on graphing paper and find the y-intercept by hand.
One of the most basic activities that you can use to help students understand the concept of slope and y-intercept is to create a story problem that illustrates the concept. For example, create a problem in which the lines on the x-axis represent months and the y-axis represents sales. Make up a scenario in which a student is selling magazines to win a prize. Give the students data points representing months and sales and ask them to find the month where the student has sold enough magazines to earn the prize, which is represented by the y-intercept.