Linear equations  (Page 3/6)

In order to find the slope of this line, we will choose any two points on this line.

Again, the selection of x and y intercepts seems to be a good choice. The x-intercept is (3, 0), and the y-intercept is (0, 2). Therefore, the slope is

The graph below shows the line and the intercepts: $x$ and $y$ .

We again find two points on the line. Say (0, 2) and (1, 5).

Therefore, the slope is $m=\frac{5-2}{1-0}=\frac{3}{1}=3$ .

Look at the slopes and the y-intercepts of the following lines.

It is no coincidence that when an equation of the line is solved for $y$ , the coefficient of the $x$ term represents the slope, and the constant term represents the y-intercept.

In other words, for the line $y=\text{mx}+b$ , $m$ is the slope, and $b$ is the y-intercept.

We solve for $y$ .

The $\text{slope}=\text{the coefficient of the }x\text{ term}=-2/3$

The $\text{y-intercept}=\text{the constant term}=2$ .

In the last section we learned that the equation of a line whose slope = m and y-intercept = b is $y=\text{mx}+b$ .

Since $m=5$ , and $b=3$ , the equation is $y=\mathrm{5x}+3$ .

Since $m=3$ , the partial equation is $y=\mathrm{3x}+b$ .

Now $b$ can be determined by substituting the point (2, 7) in the equation $y=\mathrm{3x}+b$ .

Therefore, the equation is $y=\mathrm{3x}+1$ .

So the partial equation is $y=\mathrm{3x}+b$

Now we can use either of the two points (–1, 2) or (1, 8), to determine $b$ .

Substituting (–1, 2) gives

So the equation is $y=\mathrm{3x}+5.$

x-intercept = 3, and y-intercept = 4 correspond to the points (3, 0), and (0, 4), respectively.

So the partial equation for the line is $y=-4/\mathrm{3x}+b$

Substituting (0, 4) gives

Therefore, the equation is $y=-4/\mathrm{3x}+4$ .