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Find the equation of the line that has a slope of -8 and passes through the point (-1,-5) write the equation in standard form.
Step 1. The slope-intercept form is given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b). From the slope intercept form we can derive the standard form given as Ax+By=C where A, B, and C are constants. Now, let's find the equation of the line in slope-intercept form
Step 2. Here, we have to find the line with slope m=-8 going through point (-1,-5).
Step 3. Given two points (x1,y1) and (x2,y2), then the slope m is given as
Step 4. Let (x1,y1)=(-1,-5) or x1=-1 and y1=-5. Let other point be (x2,y2)=(x,y) or x2=x and y2=y.
Step 5. Now we're given
. Substituting above values and variables in the slope equation m yields the following steps:
Step 6. Multiply x+1 to both sides to get rid of denominator on right side of equation.
Step 7. Add -5 to both sides of the equation
Step 7. The equation in slope-intercept form is
where the slope m=-8 and the y-intercept b=-13.
Note: the above equation can be rewritten in standard form by adding 8x to both sides of the equation.
Step 8. ANSWER: The equation of the line in standard form is
And the graph is shown below which is consistent with the above steps.
I hope the above steps and explanation were helpful.
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