Can you explain the relationship between the graph of a line and its equation ?

Question

Also,I need to know the meaning of a slope as a constant rate of change and y-intercept in real-life situations.

Answer 1

Well a straight horizontal line represents a y=integer equation.
a straight non-horizontal line represents a first degree equation (x is in the first degree).
a bent line represents a second or more degree equation.
The slope represents the (m) in the equation y=mx+b
for the graph the slope is rise/run

slope is a constant rate could be represented as a car moving with a constant speed. On a distance/time graph the equation would be a straight non-horizontal line. When this line intercepts the y-axis then this would be our starting time or t=0. In other words we start our timing from the "y" where the line intercepts the y-axis.

Answer 2

Assuming the equation is in slope-intercept form y = mx + b,

m is the slope of the line (rise over run). If m is 2, then line increases 2 units in the y-direction for every unit in the x-direction.

b is the y-intercept. This is the value of y when x equals zero. It is the value of the line where it hits the y-axis.

Rates of change (slope) and initial states (y-intercept): slope could be defined as the rate of change. For example, if you have a graph of the water level in a bathtub which is being filled, with the x-variable being time and the y-variable being the water level in inches, the line will go up and to the right--as you allow more time, the tub gets fuller. If you fill the tub faster the line will be steeper. The slope is equivalent to the rate of change of the water level in the tub. The y-intercept represents the amount of water that was in the tub when you started to fill it. If the tub was empty at time = zero, then the y-intercept is zero. If you started out with say 1-inch of water in the tub, then the y-intercept is 1.

Answer 3

The equation of a line, when solved for the independent variable, will look like this:

y = mx+b

m is the line's slope, and b is the y-intercept of the slope (or where it crosses the y-axis).

If a car travels at a constant speed, then the slope would represent it's distance traveled per unit of time.
If another car travels at the same speed, but started off with a "lead" on the first car (like it left at the same time but one mile ahead), then the y-intercept would represent the initial position or "lead" of the second car.

Answer 4

Normally the y intercept is value of y when x or t is zero - for example if a gun is fired, y might be the muzzle velocity at time 0 or y might be the height from which it is fired when x starts at zero. Solving the equation for the two values when each one is zero give the crossing points for the axes, like when it hits ground or when height or speed is zero.

Answer 5

all the points satisfying the function form the graph of that function.

slope is tangent value of the angle between x axis and the line
or tangent line of the curve.

y-intercept is a point (0,y)

Answer 6

for a straight line:

y = m*x + b

where m is the slope (rise/run)

b is the y-intercept (where the line hits the y-axis)

and y and x are variables. if you have m and b, you can plug in an x to see where its y is. and vice versa.