I need to write an equation of the line containing the given point and parallel to the given line. in y = mx+b.
(-6,2;) 6x=5y+4
the slope of the given line is 6/5
so new equation is y = (6/5)x + b
but (-6,2) lies on it
2 = -36/5 + b
10 + 36 = 5b
b = 46/5
y = (6/5)x + 46/5
ok, thank you so much!
To write the equation of a line in the form y = mx + b, we need to determine the slope (m) and the y-intercept (b) of the line.
Given the equation of the line 6x = 5y + 4, let's rearrange it and put it in slope-intercept form (y = mx + b).
Step 1: Rearrange the equation for y
We want to isolate y on one side of the equation, so let's start by subtracting 4 from both sides:
6x - 4 = 5y
Step 2: Divide both sides by 5
To solve for y, we need to isolate it completely. Divide both sides of the equation by 5:
(6/5)x - (4/5) = y
Now, we have y in terms of x: y = (6/5)x - (4/5).
Step 3: Find the slope (m)
The slope of the given line is the coefficient of x in the equation. In this case, the slope is 6/5, which means any line parallel to this will have the same slope.
Step 4: Write the equation of the line
We have the slope (m = 6/5), and we are given the point (-6, 2). To find the equation of the line parallel to the given line and passing through this point, we can plug in the values into the point-slope formula:
y - y1 = m(x - x1)
Using the point (-6, 2) and the slope 6/5, the equation becomes:
y - 2 = (6/5)(x - (-6))
Simplifying further yields:
y - 2 = (6/5)(x + 6)
Finally, expanding the right side gives us the equation in the slope-intercept form:
y - 2 = (6/5)x + (36/5)
So, the equation of the line containing the point (-6, 2) and parallel to the given line 6x = 5y + 4 is y = (6/5)x + (36/5).