Find the equation of each line
a) with an x intercept the same as 2x-5y=10 and parallel to x=4
b) with an x-intercept of -4 and a y-intercept of 6
please help me, I have no idea how to do these
nevermind, after reading ahed in my maths book, I think I'm finally starting to get it; still, thank you for always helping me whenever I don't understand my homework! :)
Sure! I can help you find the equations of the lines.
a) To find the equation of a line with a given x-intercept and parallel to another line, we need to understand the relationship between parallel lines.
Two lines are parallel if they have the same slope. So, first, let's find the slope of the given line 2x - 5y = 10.
To find the slope, we need to rearrange the equation into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Let's rearrange 2x - 5y = 10:
2x - 5y = 10
-5y = -2x + 10 (subtract 2x from both sides)
y = (2/5)x - 2 (divide by -5)
So, the slope of the given line is 2/5.
Now, since we want to find a line parallel to x = 4, which is a vertical line, we can directly say that its slope is undefined because vertical lines have no slope.
So, the line we are looking for will also have an undefined slope.
Now, we know that the x-intercept is the value of x when y is zero. From the given equation x = 4, we can see that it crosses the x-axis at x = 4. Therefore, the x-intercept is (4, 0).
To find the equation, we can use the point-slope form of a line:
y - y1 = m(x - x1)
Since our slope is undefined, our equation will be in the form x = a, where 'a' is the x-coordinate of the x-intercept.
So, the equation of the line parallel to x = 4 and with an x-intercept of (4, 0) is: x = 4.
b) To find the equation of a line with given x-intercept and y-intercept, we need to understand the slope-intercept form (y = mx + b) of a line.
The slope-intercept form of a line allows us to find the equation when we know the slope (m) and the y-intercept (b).
In this case, we're given the x-intercept as -4 and the y-intercept as 6.
To find the slope, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Since we know the y-intercept is (0, 6), we can use that as our second point on the line. Let's say our first point is the x-intercept (-4, 0).
m = (0 - 6) / (-4 - 0)
m = -6/-4
m = 3/2
So, the slope of the line is 3/2.
Now, substitute the slope (m = 3/2) and the y-intercept (b = 6) into the slope-intercept form (y = mx + b):
y = (3/2)x + 6
Therefore, the equation of the line with an x-intercept of -4 and a y-intercept of 6 is: y = (3/2)x + 6.