The equation of a line iswith m being the slope and b being the y intercept. The y-intercept is at, so. The x-intercept is, so after plugging in the equation becomes, simplifying to.

The equation of a line is, with m being the slope of the line, and b being the y-intercept. The y intercept of the line is at, so.

The x-intercept is at, the equation becomes, simplification yields

A horizontal line has equationfor some value of; since the line goes through a point with-coordinate 3, the line is. Also, since the line is solid and the region above this line is shaded in, the corresponding inequality is.

A vertical line has equationfor some value of; since the line goes through a point with-coordinate 4, the line is. Also, since the line is solid and the region right of this line is shaded in, the corresponding inequality is.

Since only the region belonging tobothsets is shaded - that is, their intersection is shaded - the statements are connected with "and". The correct choice is.

First, we determine the equation of the boundary line. This line includes pointsand, so the slope can be calculated as follows:

Since we also know the-intercept is, we can substitutein the slope-intercept form to obtain the equation of the boundary line:

The boundary is included, as is indicated by the line being solid, so the equality symbol is replaced by eitheror. To find out which one, we can test a point in the solution set - for ease, we will choose:

_____

_____

_____

0 is less than 3 so the correct symbol is.

The inequality is.

First, we determine the equation of the boundary line. This line includes pointsand, so the slope can be calculated as follows:

Since we also know the-intercept is, we can substitutein the slope-intercept form to obtain equation of the boundary:

The boundary is excluded, as is indicated by the line being dashed, so the equality symbol is replaced by eitheror. To find out which one, we can test a point in the solution set - we will choose:

_____

_____

_____

_____

1 is greater than 0 so the correct symbol is

The inequality is

This function is linear (a line), so we must remember that we can represent lines algebraically using y=mx+b, where m is the slope and b is the y-intercept.

Looking at the graph, we can tell immediately that the y-intercept is -5, because the line crosses(intercepts) the y-axis at -5.

To find the slope, we need two points,and the following formula:

.

For the sake of the example, choose (0,-5) and (2,-1). We can see that the graph clearly passes through each of these points. Any two points will do, however. Substituting each of the values into the slope formula yields m=2.

Thus, our final answer is

线是垂直的山坡时,negative recicprocals of each other such as. To find the slope of our equation we must change it to slope y-intercept form.

Subtract the x variable from both sides:

Divide by 4 to isolate y:

The negative reciprocal of the above slope:. The only equation with this slope is.

To find where this equation crosses theaxis or its-intercept, change the equation into slope intercept form.

Subtract to isolate:

Divide both sides byto completely isolate:

This form is the slope intercept formwhereis the slope of the line andis the-intercept.

To find the x-intercepts, remember that the line is crossing the x-axis, and that y=0 when the line crosses the x-axis.

So plug in y=0 into the equation above.

To find the y-intercepts, remember that the line is crossing the y-axis, and that x=0 when the line crosses the x-axis.

So plug in x=0 into the equation above.

斜率是一条线的变化。找到这条线啊ne can remember it as rise over run. This rise over run is really the change in the y direction over the change in the x direction.

Therefore the formula for slope is as follows.

Plugging in our given points

and