Question 283026
The slope-intercept form is: y = mx+b, where m is the slope and b is the y-intercept (the point were x=0).
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The slope is defined as the rise over the run, which is the change in 'y' divided by the change in 'x'.
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m = (y<sub>2</sub>-y<sub>1</sub>)/x<sub>2</sub>-x<sub>1</sub>)
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(x<sub>1</sub>,y<sub>1</sub>) = (5,4)
(x<sub>2</sub>,y<sub>2</sub>) = (-4,-3)
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m = (-3 -4)/(-4-5)
m = -7/-9 = 7/9
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y = 7/9x + b
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Substitute what we know already to find 'b'.
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For example, we know the point (5,4) is on the line.
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4 = 7/9(5) + b
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Multiply through by 9 to remove the fraction
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36 = 7(5) + 9b
36 = 35 + 9b
1 = 9b
9b = 1
b = 1/9
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Now we can find the x-intercept, which is the point where y=0.
0 = 7/9x + 1/9
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multiply through by 9
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9(0) = 7x + 1
0 = 7x + 1
x = -1/7
(-1/7,0)
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So, to summarize:
Equation is:  y = 7/9x + 1/9
y-intercept is:  (0, 1/9)
x-intercept is:  (-1/7, 0)
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Graphing it helps confirm your work.
{{{graph(500,500,-6,6,-6,6,7/9*x+1/9)}}}
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Done