The equation for line is [tex]y=-\frac{3}{4} x-\frac{3}{2}[/tex]
Explanation:
It is given that the line passes through the point [tex](2,-3)[/tex] with x-intercept = -2
The x intercept is the value of x when y = 0.
Thus, it can be written in coordinate as [tex](-2,0)[/tex]
Now, we shall determine the slope using the points [tex](2,-3)[/tex] and [tex](-2,0)[/tex]
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substituting, we get,
[tex]m=\frac{0+3}{-2-2} \\m=-\frac{3}{4}[/tex]
Thus, the slope is [tex]m=-\frac{3}{4}[/tex]
Now, we shall substitute the point [tex](2,-3)[/tex] and slope [tex]m=-\frac{3}{4}[/tex] in the point-slope formula [tex]y-y_1=m(x-x_1)[/tex], we get,
[tex]y+3=-\frac{3}{4} (x-2)[/tex]
Multiplying both sides by 4, we get,
[tex]4y+12=-3x+6[/tex]
Subtracting both sides by 12,
[tex]4y=-3x-6[/tex]
Dividing both sides by 4, we get,
[tex]y=-\frac{3}{4} x-\frac{3}{2}[/tex]
Thus, the equation of the line is [tex]y=-\frac{3}{4} x-\frac{3}{2}[/tex]
