Write an equation of a line whose graph is parallel to the graph of y = 3x – 10.
y = 3x
To find the equation of a line parallel to y = 3x – 10, we know that the slope (m) of the new line will be the same as the given line. In this case, the slope is 3.
The general equation of a line is y = mx + b, where m is the slope and b is the y-intercept.
Since we need a line parallel to y = 3x – 10, we will have the same slope, m = 3. Therefore, the equation of the line will be y = 3x + b, where b is the y-intercept that we need to find.
To find the y-intercept, we can use a point from the given line. Let's use the y-intercept of the given line, which is (0, -10).
Substituting the values (0, -10) into the equation y = 3x + b, we can solve for b:
-10 = 3(0) + b
-10 = 0 + b
b = -10
Therefore, the equation of the line parallel to y = 3x – 10 is y = 3x - 10.
To find an equation of a line parallel to the graph of y = 3x - 10, we need to keep the same slope. In this case, the slope of the given line is 3.
The equation of a line can be written in the form y = mx + b, where m represents the slope and b represents the y-intercept.
Since the line we want is parallel to y = 3x - 10, the new equation will have the same slope of 3. Now we need to find the y-intercept.
To find the y-intercept, we need a point that the line passes through. Let's choose a simple point, such as the origin (0,0).
Using the slope-intercept form, we can substitute the point (0,0) and the slope (3) into the equation:
y = mx + b
0 = 3(0) + b
0 = 0 + b
b = 0
Since b is 0, the equation of the line parallel to y = 3x - 10 is:
y = 3x + 0
y = 3x