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Use the given conditions to write an equation for the line in point-slope form. Passing through (2,-3) with x-intercept = -2

User Powlo
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The equation for line is
y=-(3)/(4) x-(3)/(2)

Step-by-step explanation:

It is given that the line passes through the point
(2,-3) with x-intercept = -2

The x intercept is the value of x when y = 0.

Thus, it can be written in coordinate as
(-2,0)

Now, we shall determine the slope using the points
(2,-3) and
(-2,0)


m=(y_2-y_1)/(x_2-x_1)

Substituting, we get,


m=(0+3)/(-2-2) \\m=-(3)/(4)

Thus, the slope is
m=-(3)/(4)

Now, we shall substitute the point
(2,-3) and slope
m=-(3)/(4) in the point-slope formula
y-y_1=m(x-x_1), we get,


y+3=-(3)/(4) (x-2)

Multiplying both sides by 4, we get,


4y+12=-3x+6

Subtracting both sides by 12,


4y=-3x-6

Dividing both sides by 4, we get,


y=-(3)/(4) x-(3)/(2)

Thus, the equation of the line is
y=-(3)/(4) x-(3)/(2)

User Khusrav
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