help Determine the equation for this diagram
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Recall the formula for a line as a function of [MATH]x[/MATH]:
[MATH]m[/MATH] is the "rise over run" slope of the line: the amount by which it moves "up" for each unit that it moves "right". This function visibly passes through points
(-1, -4) and (1, 2), making its slope [MATH]m = \frac{2 - (-4)}{1 - (-1)} = \frac{6}{2} = 3[/MATH].
[MATH]b[/MATH] is the y-intercept: the location on the Y axis where the line crosses (when [MATH]x = 0[/MATH]). In the graph, this can be seen as [MATH]b = -1[/MATH]. This can also be calculated with [MATH]b = y - mx[/MATH] using any valid pair of coordinates.
The graph represents the axes with different scales, with Y being squashed (or X being stretched), making it appear that the line has a slope less than 1. Don't be confused by the appearance of the graph: focus on the numbers.
Recall the formula for a line as a function of [MATH]x[/MATH]:
[MATH]y = mx + b[/MATH]
[MATH]m[/MATH] is the "rise over run" slope of the line: the amount by which it moves "up" for each unit that it moves "right". This function visibly passes through points
(-1, -4) and (1, 2), making its slope [MATH]m = \frac{2 - (-4)}{1 - (-1)} = \frac{6}{2} = 3[/MATH].
[MATH]b[/MATH] is the y-intercept: the location on the Y axis where the line crosses (when [MATH]x = 0[/MATH]). In the graph, this can be seen as [MATH]b = -1[/MATH]. This can also be calculated with [MATH]b = y - mx[/MATH] using any valid pair of coordinates.
The graph represents the axes with different scales, with Y being squashed (or X being stretched), making it appear that the line has a slope less than 1. Don't be confused by the appearance of the graph: focus on the numbers.
HallsofIvy
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A very slightly different way: Yes, any (non-vertical) line can be written y= ax+ b. Since I don't like to work with fractions I note that the line passes through the points (1, 2) and (3, 8). When x= 1, y= 2 so 2= a(1)+ b. When x= 3, y= 8 so 8= a(3)+ b.
To solve the two equations 2= a+ b and 8= 3a+ b, subtract the first equation from the second to eliminate b: 6= 2a so a= 3. (That's exactly the same calculation Mr. Bland did to find the slope.) Then 2= 3+ b so b= -1.
y= 3x- 1
To solve the two equations 2= a+ b and 8= 3a+ b, subtract the first equation from the second to eliminate b: 6= 2a so a= 3. (That's exactly the same calculation Mr. Bland did to find the slope.) Then 2= 3+ b so b= -1.
y= 3x- 1
Harry_the_cat
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D0skey, if you explain how YOU got your answer, we can see where you are going wrong and help you more.