Core Focus on Linear Equations Lesson 3.3 Core Focus on Linear Equations Writing Linear Equations From Key Information

Warm-Up Graph each linear equation. Clearly mark at least three points on each line. 1. 2. y = −2x

Writing Linear Equations From Key Information Lesson 3.3 Writing Linear Equations From Key Information Write a linear equation in slope-intercept form when given information about the line.

Example 1 Write the equation of a line that has a slope of −2 and a y-intercept of 5. Write the general slope-intercept equation. y = mx + b Substitute –2 for m since m represents y = –2x + b the slope. Substitute 5 for b since b represents y = –2x + 5 the y-intercept. The equation is y = –2x + 5. When you are given the slope and the y-intercept for a line you need to insert the information into y = mx + b for the appropriate values.

Writing a Linear Equation when Given Key Information Find the slope (m) of the line. Find the y-intercept (b) of the line. If necessary, substitute the slope for m and one ordered pair (x, y) for the corresponding variables in the equation y = mx + b. Solve for b. Write the equation in the form y = mx + b.

Example 2 1 = (–3) + b 1 = –4 + b +4 +4 5 = b Write the equation of a line that has a slope of and goes through the point (−3, 1). The slope is given. m = Write the slope-intercept equation y = x + b with the slope. Find the y-intercept, b, by substituting the given point (–3, 1) for x and y in the slope-intercept equation. 1 = (–3) + b 1 = –4 + b +4 +4 5 = b

Example 2 Continued… Write the equation of a line that has a slope of and goes through the point (−3, 1). Write the equation by substituting y = x + 5 m and b. Check by graphing. Plot the point (–3, 1). Use the slope to find at least two more points. Draw a line through the points.

Explore! Triangle Lines A triangle consists of three line segments. A segment is a portion of a line. Step 1 Find the equation of the line that contains AB . Step 2 Find the equation of the line that contains AC. Step 3 Find the equation of the line that contains BC. Step 4 Ryan made his own triangle. He chose three points and wants you to find the equations of the three lines that make up his triangle. His points are (3, 3), (−2, −7) and (−7, −2). Can you find the three linear equations that intersect to make his triangle? Step 5 The points where the line segments meet in a triangle are called the vertices. Graph your three lines on a piece of graph paper using the slope and y-intercepts from your equations. Does the triangle that is formed have the same three vertices that Ryan chose?

Communication Prompt How do you find the equation of a line when you are given two points the line passes through?

Exit Problems Write the equation of each line in slope-intercept form. slope = 4 y-intercept = −5 slope = goes through (2, 6) goes through (0, 4) and (−2, 8) y = 4x − 5 y = −2x + 4