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For a line, this is the x-intercept. For a polynomial, these points are the roots or solutions of the polynomial at which y=0.
A root is the value of the variable (usually, x) for which the polynomial is zero. Equivalently, a root is an x-value at which the graph crosses the x-axis.
y-(y_1)=m(x-x_1) (x_1,y_1) is the specified point on your line and "m" is the slope of your line. Hope this helps!! ^^
There is not a single line, but infinitely many lines, that pass through the point (-5, 0). One thing you can do is choose some random slope, then use the equation for an equation that goes through a point and has a specified slope.
For example, if the slope at a certain point is 1.5, you can draw a line that goes through the specified point, with that slope. The line would represent the slope at that point. If you want to graph the slope at ALL POINTS, take the derivative of the function, and graph the derivative. The derivative shows the slope of a function at all points.