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A line passes through the point (-4,-6) and has a slope of -5/2. Write an equation in slope intercept form for this line

User Besen
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1 vote

Final answer:

The equation of the line in slope-intercept form that passes through the point (-4,-6) with a slope of -5/2 is y = -5/2x + 4.

Step-by-step explanation:

To write the equation of a line in slope-intercept form, which is y = mx + b, we need to know the slope (m) and the y-intercept (b). The equation can be constructed using the slope and a point the line passes through.

In this case, we are given the slope as -5/2 and a point (-4, -6). We can use the point-slope form to first write the equation that incorporates the given point and then manipulate it into slope-intercept form. The point-slope form is (y - y1) = m(x - x1), where (x1, y1) is the given point. Substituting our values in, we get:

(y - (-6)) = -5/2(x - (-4))

Next, we distribute the slope on the right-hand side and simplify:

y + 6 = -5/2x - (-5/2 × 4)

y + 6 = -5/2x + 10

Now, to get the equation in slope-intercept form, we isolate y:

y = -5/2x + 10 - 6

y = -5/2x + 4

Therefore, the equation of the line in slope-intercept form is y = -5/2x + 4.

User PaulShovan
by
7.7k points
4 votes

Answer:

y= -5/2x-16

Step-by-step explanation:

hope it helps

hope its right :)

User Grease
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8.6k points

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