Solution - Properties of a line from two points

In slope-intercept form, $$y=mx+b$$, $$m$$ represents the slope, $$b$$ represents the y-intercept, and $$x$$ and $$y$$ represent the x and y-coordinates of a point on the line.
To find $$b$$, plug the slope ($$m$$) and the coordinates of a point on the line ($$x_1$$, $$y_1$$) into the slope-intercept formula:

$$y=mx+b$$
$$m=\frac{8}{7}$$
$$y_1=24$$
$$x_1=21$$

To find the equation of the line, plug $$m$$ and $$b$$ into the slope-intercept formula:

$$y=mx+b$$
$$m=\frac{8}{7}$$
$$b=0$$
$$y=8/7x$$

To find the x-intercept, plug 0 in for $$y$$ in the equation, $$y=mx+b$$, and solve for $$x$$:

$$\frac{8}{7}x=0$$

Divide both sides by the coefficient:

$$x=0$$

x-intercept: $$\left(0,0\right)$$

To find the y-intercept, plug 0 in for $$x$$ in the equation, $$y=mx+b$$, and solve for $$y$$:

$$y=0$$

y-intercept: $$\left(0,0\right)$$

The $$b$$ in the slope-intercept equation, $$y=mx+b$$, is always equal to the y-coordinate of the y-intercept point. In other words, if $$x=0$$ then $$y=b$$.