Question

Pls answer with a graph

Answer 1

Answer-

Slope-intercept form the line is,

$y=-x-2$

Solution-

The general slope intercept formula of a line is,

$y=mx+c$

Where,

m = slope of the line

c = y - intercept of the line

But, in this case, the coordinate of a point and y-intercept is given. As both the points i.e the given point and the y-intercept lie on the line, we can get the equation the line by two point formula, i.e

$\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}$

Taking (2, -4) and (0, -2) as two points,

$\frac{y+4}{-2+4}=\frac{x-2}{0-2}$

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

$y+4=-(x-2)$

$y+4=-x+2$

$y=-x-2$

Comparing this equation with the slope-intercept equation, we get that m = slope = -2 and y = -2 (as given)

So this equation is the slope intercept form of the line.