Find the equation of the line using the slope formula. write the final equation using the slope-intercept form. the x- intercept is 1, and (x, y) = ( -2, 12) is a point on the line

Step-by-step explanation:

The slope formula for a straight line is:

Where, 'm' is the slope and 'b' is the y-intercept.

To find the x-intercept of a line, we need to equal 'y' to zero, and then solve for 'x'. In this case we know that the x-intercept is 1, so we have the point (x1, y1)=(1,0). We are given a second point which is: (x0, y0)=(-2, 12).

To find the slope, we use the following formula:

Now, The equation of the line is: y - y0 = m(x-x0). Then, substituting the values of 'm', 'x0' and 'y0' we have that:

The equation of the line using the slope-intercept form is:

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is