Module 11-3 Objectives Graph a line and write a linear equation using point-slope form. Write a linear equation given two points.

If you know the slope and any point on the line, you can write an equation of the line by using the slope formula. For example, suppose a line has a slope of 3 and contains (2, 1) . Let (x, y) be any other point on the line. Substitute into the slope formula. Multiply both sides by (x - 2). Simplify.

Additional Example 1A: Writing Linear Equations in Point-Slope Form Write an equation in point slope form for the line with the given slope that contains the given point. y – y1 = m (x – x1) Write the point-slope form.

Additional Example 1B: Writing Linear Equations in Point-Slope Form Write an equation in point slope form for the line with the given slope that contains the given point. slope = –4; (0, 3) y – y1 = m(x – x1) Write the point-slope form. Substitute –4 for m, 0 for x1 and 3 for y1. y – 3 = –4(x – 0) y – 3 = –4(x – 0)

In the previous lesson, you graphed a line given its equation in slope-intercept form. You can also graph a line when given its equation in point-slope form. Start by using the equation to identify a point on the line. Then use the slope of the line to identify a second point.

Additional Example 2A: Using Point-Slope Form to Graph Graph the line described by the equation. y – 1 = 2(x – 3) (2,5) y – 1 = 2(x – 3) is in the form y – y1= m(x – x1). (1,3) The line contains the point (3, 1). Step 1 Plot (3, 1). Step 2 Count 2 units up and 1 unit right and plot another point. Step 3 Draw the line connecting the two points.

Additional Example 2B: Using Point-Slope Form to Graph Graph the line described by the equation. (2,7) y – 4 = (x – (–2)) is in the form y – y1= m(x – x1). (-2,4) The line contains the point (–2, 4). slope: m = Step 1 Plot (–2, 4). Step 2 Count 3 units up and 4 units right and plot another point. Step 3 Draw the line connecting the two points.

Additional Example 3A: Writing Linear Equations in Slope-Intercept Form Write the equation that describes each line in slope-intercept form. Slope = 3, (–1, 4) is on the line. Step 1 Write the equation in point-slope form: y – y1 = m(x – x1) y – 4 = 3[x – (–1)] Step 2 Write the equation in slope-intercept form by solving for y. Rewrite subtraction of negative numbers as addition. y – 4 = 3(x + 1) Distribute 3 on the right side. y – 4 = 3x + 3 + 4 + 4 Add 4 to both sides. y = 3x + 7

Additional Example 3B: Writing Linear Equations in Slope-Intercept Form Write the equation that describes the line in slope-intercept form. (2, –3) and (4, 1) Step 1 Find the slope. Step 2 Substitute the slope and one of the points into the point-slope form. y – y1 = m(x – x1) y – (–3) = 2(x – 2) Choose (2, –3).

Additional Example 3B Continued Write an equation in slope-intercept form for the line through the two points. (2, –3) and (4, 1) Step 3 Write the equation in slope-intercept form. y + 3 = 2(x – 2) y + 3 = 2x – 4 –3 –3 y = 2x – 7

Additional Example 3C: Writing Linear Equations in Slope-Intercept Form Write the equation that describes the line in slope-intercept form. Step 2 Find the slope.

Additional Example 3C Continued Write the equation that describes the line in slope-intercept form. Step 3 Write the equation in slope-intercept form. y = mx + b Write the slope-intercept form. y = –4x + 1 Substitute –4 for m and 1 for b.

Tonight’s HW Page 304 #3-12 all