Write an equation of a line that is parallel to y = 3x – 5 and goes through the point (3, 1).
a line parallel to y = 3x - 5 must look like
y = 3x + b, that is, it can only differ in the constant, the slope stays the same.
So we need to find that constant b.
But we know that (3,1) lies on it, so
in y = 3x + b
1 = 3(3) + b
b = -8
new equation: y = 3x - 8
To find an equation of a line parallel to another line, we need to know that parallel lines have the same slope.
Given that the original line is y = 3x - 5, we can determine that its slope is 3.
Now, let's use the point-slope form of a linear equation to find the equation of the parallel line that goes through the point (3, 1).
The point-slope form of a linear equation is:
y - y1 = m(x - x1)
where:
- y and x are the coordinates of any point on the line,
- y1 and x1 are the coordinates of a specific point on the line, and
- m is the slope of the line.
We can substitute the values of the given point (3, 1) and the slope of the original line (m = 3) into the point-slope form.
y - 1 = 3(x - 3)
Now, let's simplify the equation:
y - 1 = 3x - 9
Finally, let's rearrange the equation to the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept:
y = 3x - 8
Therefore, the equation of a line that is parallel to y = 3x - 5 and goes through the point (3, 1) is y = 3x - 8.