y – y1 = m (x – x1) Point-Slope Form When we know the slope and any point on the line, we can use POINT-SLOPE FORM. y – y1 = m (x – x1)

Write an equation in point-slope form for the line with the given slope that contains the given point. slope: ⅙; (5, 1) y – y1 = m (x – x1) slope: -1; (-1, -4) y – y1 = m (x – x1)

Try It slope: 2; (½, 1) slope: 0; (3, -4)

Using point-slope form to graph a line Graph the line described by the equation y – 1 = 2 (x – 3). Step 1: Step 2: Step 3:

Using point-slope form to graph a line Graph the line described by the equation y – 4 = ¾ (x + 2). Point: Slope:

Try it! y + 2 = -(x – 2) y + 3 = 0 (x – 4) Point: Slope: Point: Slope:

Slope of - 3 and point (4, 7) Slope of 𝟐 𝟓 and point (10, -8) Example 1 Write the point-slope equation of the line with the given slope that passes through the given point. Slope of - 3 and point (4, 7) Slope of 𝟐 𝟓 and point (10, -8)

Example 2 Graph the line given the equation below. y – 3 = 𝟐 𝟓 (x – 1)

Example 3 Graph the line given the equation below. y – 2 = - 𝟏 𝟑 (x + 4)

Example 4 Write the equations of the line (point-slope, slope intercept and standard) given two points on the line. (-8, 7) and (8, 15)

Example 5 Write the equations of the line (point-slope, slope intercept and standard) given two points on the line. (12, -4) and (16, 1)

Example 6 Write the equations of the line (point-slope, slope intercept and standard) given two points on the line. (6, 11) and (3, 13)

Example 7 Is the relationship shown by the linear Example 7 Is the relationship shown by the linear? If it is write an equation in point-slope and slope-intercept form. X Y -3 3 6 12 8 21 11

Example 8 Is the relationship shown by the linear Example 8 Is the relationship shown by the linear? If it is write an equation in point-slope and slope-intercept form. X Y 5 11 8 16 12 25 17 37

What if you are asked to write the equation in slope-intercept form What if you are asked to write the equation in slope-intercept form? (2 additional steps) Write the equation that describes the line in slope-intercept form. Slope = 3; (-1, 4) Write the equation that describes the line in slope-intercept form. Slope = -1/2; (6, -7)

Let’s build on to what we already know… Step 1: Step 2: Step 3: Write an equation that describes the line in slope-intercept form. (2, -3) and (4, 1)

Write the equation that describes the line in slope-intercept form. (1, -2) and (3, 10) (2, 15) and (-4, -3)

Warm Up Given the two points, find the point slope, slope intercept and standard form of the linear equation. Then graph. (6, 6) and (12, 8)