Question

in the equation d = 60t, the number 60 represents the ____. the graphical representation of the equation y = 3x is a __ line. the point where the graph of a proportional relationship intersects the y - axis is called the __. in the equation d = 65t, d stands for ____.

Explanation:

First Question:

Step1: Recall the formula for distance

The formula for distance is \( D = \text{speed} \times T \) (where \( T \) is time). In the equation \( D = 60T \), comparing with the distance - speed - time formula \( D=vT \) (where \( v \) is speed), the number 60 represents the speed.

Step1: Recall the form of a linear equation

The equation of a line in slope - intercept form is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. For the equation \( y = 3x \), we can rewrite it as \( y=3x + 0 \), where \( m = 3 \) (slope) and \( b = 0 \) (y - intercept). The graph of an equation of the form \( y=mx + b \) is a straight line. Since \( b = 0 \), the line passes through the origin. So the graphical representation of \( y = 3x \) is a straight (or a proportional) line.

Step1: Recall the properties of proportional relationships

A proportional relationship can be written in the form \( y=kx \) (where \( k\) is the constant of proportionality) or in the general linear form \( y = mx + b \) with \( b = 0 \). The point where a graph intersects the \( y \) - axis is found by setting \( x = 0 \). For a proportional relationship \( y=kx \), when \( x = 0 \), \( y=0 \). The point where a graph intersects the \( y \) - axis is called the y - intercept. In the case of a proportional relationship, the y - intercept is 0 (the origin), but the name of the point where the graph intersects the \( y \) - axis is the y - intercept.

Answer:

speed

Second Question: