Lesson 11.5 Using Intercepts

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Presentation transcript:

Lesson 11.5 Using Intercepts Essential Question: How do you find the x- and y-intercept of a linear equation?

Before we start… What do you notice about the graph of this line?

When graphing a line… The fact is that you only need 2 points to determine a line. Two convenient points to use are the points where the graph crosses the axes.

What is an intercept? Crosses the y -axis. Crosses the x -axis.

What are the intercepts? y-Intercept – where the graph intersects the y-axis It’s the y-coordinate of the intersecting point. (0, y) x-Intercept – where the graph intersects the x-axis It’s the x-coordinate of the intersecting point. (x, 0) ORDERED PAIRS, (x, y)

How can I find intercepts? To find the x-intercept Let y = 0 and solve the equation for x. To find the y-intercept Let x = 0 and solve the equation for y.

Find the x and y-intercepts of the graph.

Find the x and y-intercepts of the graph. 𝑦= 1 2 𝑥−5

Find the x and y-intercepts of the graph.

Find the x and y-intercepts of the graph. 𝑦=2𝑥−10

Find the x and y-intercepts of the graph.

Why do I need intercepts? If you are given the x and y-intercepts, it is one way to graph a line. If you are given an equation in standard form, you can use intercepts to graph.

Graph the line with an x-intercept of -3 and a y-intercept of 2.

Graph the line with an x-intercept of 6 and a y-intercept of -10.

What is standard form? A, B and C are all integers and A and B are not equal to 0.

How can I graph an equation in standard form? Verify the equation is in standard form Ax + By = C Find the x-intercept Find the y-intercept Plot the intercepts on your graph. Draw a line to connect the dots.

Fitness Deena runs and walks with her dog on a trail that is 8 miles long. She can run 4 miles per hour and walk 2 miles per hour. Graph the equation 4𝑥+2𝑦=8, where x is the number of hours she runs and y is the number of hours she walks. What do the intercepts represent?

Snacks James spends $24 for cookies and ice cream Snacks James spends $24 for cookies and ice cream. Cookies cost $3 a box and ice cream costs $4 a carton. Graph the equation 3𝑥+4𝑦=24, where x is the number of cookie boxes and y is the number of ice-cream cartons. What do the intercepts represent?

How do you find the x- and y-intercept of a linear equation?

Ticket Out the Door Find the x and y-intercepts of the equation. 5𝑥−2𝑦=10