Question

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

Answer 1

The equation for line is $y=-\frac{3}{4} x-\frac{3}{2}$

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 $(-2,0)$

$m=\frac{y_2-y_1}{x_2-x_1}$

Substituting, we get,

$m=\frac{0+3}{-2-2} \\m=-\frac{3}{4}$

Thus, the slope is $m=-\frac{3}{4}$

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

$y+3=-\frac{3}{4} (x-2)$

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,

$y=-\frac{3}{4} x-\frac{3}{2}$

Thus, the equation of the line is $y=-\frac{3}{4} x-\frac{3}{2}$