The equation of a line is y=15x−7. What are the coordinates of the point where the line crosses the y-axis?
The Correct Answer and Explanation is :
To find the coordinates of the point where the line ( y = 15x – 7 ) crosses the y-axis, we need to determine the value of ( y ) when ( x = 0 ). This point is referred to as the y-intercept.
- Substituting ( x = 0 ):
We substitute ( x = 0 ) into the equation of the line:
[
y = 15(0) – 7
]
Simplifying this gives:
[
y = 0 – 7 = -7
] - Finding the Coordinates:
Therefore, the coordinates of the point where the line crosses the y-axis are:
[
(0, -7)
] - Understanding the y-axis:
The y-axis is the vertical line where ( x = 0 ) for all values of ( y ). A line crosses the y-axis only once, which occurs at the y-intercept. The y-intercept is critical because it gives us information about the behavior of the line; specifically, it indicates where the line starts when graphed. - Interpreting the Equation:
The equation ( y = 15x – 7 ) is in slope-intercept form ( y = mx + b ), where ( m ) represents the slope and ( b ) represents the y-intercept. In this case, the slope ( m = 15 ) indicates that for every unit increase in ( x ), ( y ) increases by 15 units. The y-intercept ( b = -7 ) tells us that the line crosses the y-axis at ( y = -7 ). - Graphical Representation:
If you were to graph this line, you would plot the point ( (0, -7) ) on the y-axis. From this point, you could use the slope to find other points on the line. For example, moving right 1 unit (to ( x = 1 )), the line would rise 15 units to ( y = 8 ).
In conclusion, the coordinates of the point where the line ( y = 15x – 7 ) crosses the y-axis are ( (0, -7) ). This point serves as a crucial reference for understanding the line’s behavior and position in the Cartesian plane.