Answer:
Slope = [tex]-1[/tex]
y-intercept = [tex]-2[/tex]
Slope-intercept equation: [tex]y=-1x-2[/tex]
Step-by-step explanation:
Let [tex]m[/tex] equal slope.
Start with:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
For Point (0,-2):
[tex]x_1=0[/tex], [tex]y_1=-2[/tex]
For Point (-5,3):
[tex]x_2=-5[/tex], [tex]y_2=3[/tex]
Let's substitute those values in.
[tex]m=\frac{3-(-2)}{-5-0}[/tex]
Rewrite.
[tex]m=\frac{3+2}{-5-0}[/tex]
Combine like terms.
[tex]m=\frac{5}{-5}[/tex]
Simplify.
[tex]m=-1[/tex]
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Let [tex]b[/tex] equal the y-intercept.
Since we have our slope, let's format an equation as:
[tex]y=mx+b[/tex]
Substitute.
[tex]y=-1x+b[/tex]
We can use either point for this next part, let's use point (-5,3).
Since the numbers are representatives of both [tex]x[/tex] & [tex]y[/tex], we can substitute:
[tex]3=-1(-5)+b[/tex]
Multiply.
[tex]3=5+b[/tex]
Subtract [tex]5[/tex] from both sides of the equation.
[tex]-2=b[/tex]
Let's rewrite.
[tex]b=-2[/tex]
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Now that we have both our slope & y-intercept, let's put this into slope-intercept form.
[tex]y=mx+b[/tex]
Substitute.
[tex]y=-1x-2[/tex]
