linear functions: point - slope form...linear functions: point - slope form given the slope of a...
TRANSCRIPT
![Page 1: Linear Functions: Point - Slope Form...Linear Functions: Point - Slope Form Given the slope of a line and a coordinate you can write a linear equation that is equivalent to the slope](https://reader036.vdocuments.mx/reader036/viewer/2022071501/6120af44df941c267d461b09/html5/thumbnails/1.jpg)
Linear Functions:Point - Slope Form
![Page 2: Linear Functions: Point - Slope Form...Linear Functions: Point - Slope Form Given the slope of a line and a coordinate you can write a linear equation that is equivalent to the slope](https://reader036.vdocuments.mx/reader036/viewer/2022071501/6120af44df941c267d461b09/html5/thumbnails/2.jpg)
Given the slope of a line and a coordinate you can write a linear equation that is equivalent to the slope - intercept form.
![Page 3: Linear Functions: Point - Slope Form...Linear Functions: Point - Slope Form Given the slope of a line and a coordinate you can write a linear equation that is equivalent to the slope](https://reader036.vdocuments.mx/reader036/viewer/2022071501/6120af44df941c267d461b09/html5/thumbnails/3.jpg)
y - y1 = m ( x - x1)
where (x1,y1) is a point on a nonvertical line with slope m..
Point - Slope Form of a Linear Equation
![Page 4: Linear Functions: Point - Slope Form...Linear Functions: Point - Slope Form Given the slope of a line and a coordinate you can write a linear equation that is equivalent to the slope](https://reader036.vdocuments.mx/reader036/viewer/2022071501/6120af44df941c267d461b09/html5/thumbnails/4.jpg)
m = 4 point = (8,2)
y - y1 = m (x - x1) - point-slope form y - 2 = 4 ( x - 8) - substitute the values y - 2 = 4x - 32 - distribute the 4 +2 +2 - add 2 to both sides y = 4x - 30 - slope - intercept form
Example
![Page 5: Linear Functions: Point - Slope Form...Linear Functions: Point - Slope Form Given the slope of a line and a coordinate you can write a linear equation that is equivalent to the slope](https://reader036.vdocuments.mx/reader036/viewer/2022071501/6120af44df941c267d461b09/html5/thumbnails/5.jpg)
You can also write a function rule given the coordinates of two points. First determine the slope of the line using the two points, and then write the equation by substituting one point and the slope into the point-slope form.
![Page 6: Linear Functions: Point - Slope Form...Linear Functions: Point - Slope Form Given the slope of a line and a coordinate you can write a linear equation that is equivalent to the slope](https://reader036.vdocuments.mx/reader036/viewer/2022071501/6120af44df941c267d461b09/html5/thumbnails/6.jpg)
P1 (2, -3) and P2 (6, -1), write the equation of the line in slope-intercept form.
Find the slope: m = y2 - y1 = -1 - (-3) = 2 = 1 x2 - x1 6 - 2 4 2
Use the point-slope form, y - y1 = m (x - x1), and substitute m = ½ and one of the given points, (2, -3) or (6, -1).It doesn’t matter what point you use.
Example
![Page 7: Linear Functions: Point - Slope Form...Linear Functions: Point - Slope Form Given the slope of a line and a coordinate you can write a linear equation that is equivalent to the slope](https://reader036.vdocuments.mx/reader036/viewer/2022071501/6120af44df941c267d461b09/html5/thumbnails/7.jpg)
P1 (2, -3)
y - y1 = m (x - x1) y - (-3) = ½ (x - 2) y +3 = ½ x - 1 -3 -3 y = ½ x - 4
P2 (6, -1)
y - y1 = m (x - x1) y - (-1) = ½ (x - 6) y +1 = ½ x - 3 -1 -1 y = ½ x - 4
![Page 8: Linear Functions: Point - Slope Form...Linear Functions: Point - Slope Form Given the slope of a line and a coordinate you can write a linear equation that is equivalent to the slope](https://reader036.vdocuments.mx/reader036/viewer/2022071501/6120af44df941c267d461b09/html5/thumbnails/8.jpg)
Given the graph, determine the equation of the line in standard form.
Points: P1 (-2, 3), P2 (-1, -2)
Slope: m = y2 - y1 = -2 - 3 = -5 x2 - x 1 -1 - (-2) 1
![Page 9: Linear Functions: Point - Slope Form...Linear Functions: Point - Slope Form Given the slope of a line and a coordinate you can write a linear equation that is equivalent to the slope](https://reader036.vdocuments.mx/reader036/viewer/2022071501/6120af44df941c267d461b09/html5/thumbnails/9.jpg)
y - y1 = m (x - x1) y - 3 = -5 (x - (-2)) y - 3 = -5x - 10 +3 +3 y = -5x -7 - slope intercept form 5x + y = -7 - standard form
![Page 10: Linear Functions: Point - Slope Form...Linear Functions: Point - Slope Form Given the slope of a line and a coordinate you can write a linear equation that is equivalent to the slope](https://reader036.vdocuments.mx/reader036/viewer/2022071501/6120af44df941c267d461b09/html5/thumbnails/10.jpg)
Write the equation of the line in standard form. Indicate the y-intercept.
1. m = 3 through (5, 2)2. m = -⅖ throught (0,5)3. m = -6 through (30, 40)
You try!
Write in slope-intercept form.
4. y - 3 = 2(x -5)5. y + 7 = ½ (x - 1)6. y - 0 = -3(x + 8)
![Page 11: Linear Functions: Point - Slope Form...Linear Functions: Point - Slope Form Given the slope of a line and a coordinate you can write a linear equation that is equivalent to the slope](https://reader036.vdocuments.mx/reader036/viewer/2022071501/6120af44df941c267d461b09/html5/thumbnails/11.jpg)
![Page 12: Linear Functions: Point - Slope Form...Linear Functions: Point - Slope Form Given the slope of a line and a coordinate you can write a linear equation that is equivalent to the slope](https://reader036.vdocuments.mx/reader036/viewer/2022071501/6120af44df941c267d461b09/html5/thumbnails/12.jpg)