Write an equation of the line satisfying the given condition.
a) x intercept = 3 y intercept=-2
I am really not sure how to start here.
b) vertical line containing (5,-1)
Would it be y=5x-1?
c) parallel to the line 3x-4y=5 and containing the points (3,-6) .
I know that the line has to have the same slope as the one about.
d) Find the slope and y intercept of the line 4x-6y=-3
To find the y value would i plug in zero for the x and solve? And then I can find the slope?
a) isn't the information like being given two points?
(3,0), (0,-2)
So just find the slope and you know the y-intercept, so
y = mx -2
b) a vertical slope has an undefined slope
It's equation will simply be x = ? (whatever the x of the given point is)
So x = 5
c) real easy
since it has the same slope the new equation must also start with
3x - 4y = k, where k is the only number that will differ.
sub in your given point to find k, and you are done
d) rearrange 4x - 6y = -3 to the form y= mx + b
-6y = -4x - 3
divide by -6
y = (-4/-6)x -3/-6
y = (2/3)x + 1/2
Thank You!!
a) To find the equation of a line given the x-intercept and y-intercept, you can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
Given the x-intercept is 3 and the y-intercept is -2, we can directly plug these values into the equation. The x-intercept is the point where the line intersects the x-axis, meaning the y-coordinate is 0. Similarly, the y-intercept is the point where the line intersects the y-axis, meaning the x-coordinate is 0.
So, plugging those values into the slope-intercept form, we get:
0 = m(3) + (-2)
Simplifying the equation, we get:
0 = 3m - 2
Now, you can solve for m:
3m = 2
m = 2/3
Finally, substitute the value of m into the equation:
y = (2/3)x - 2
b) To find the equation of a vertical line containing a given point, you need to use the equation x = k, where k is the x-coordinate of the given point.
In this case, the given point is (5, -1), so the equation would be:
x = 5
c) To find the equation of a line that is parallel to a given line and passes through a given point, you need to find the slope of the given line and then use the point-slope form of a linear equation.
The given line is 3x - 4y = 5, and we need to find a line parallel to it that contains the point (3, -6).
To find the slope of the given line, we can rewrite it in slope-intercept form y = mx + b:
3x - 4y = 5
-4y = -3x + 5
y = (3/4)x - (5/4)
The slope of this line is (3/4). Since the desired line is parallel to this line, it will also have a slope of (3/4).
Now, we can use the point-slope form of a linear equation to find the equation of the parallel line:
y - y1 = m(x - x1)
Substituting the values of (x1, y1) = (3, -6) and m = (3/4), we get:
y - (-6) = (3/4)(x - 3)
y + 6 = (3/4)x - (9/4)
y = (3/4)x - (9/4) - 6
y = (3/4)x - 15/4
d) To find the slope and y-intercept of a given line, you need to rewrite the equation in slope-intercept form, y = mx + b.
Given the line 4x - 6y = -3, you can solve for y algebraically:
-6y = -4x - 3
y = (4/6)x + (3/6)
y = (2/3)x + (1/2)
Now, you can see that the slope (m) is (2/3) and the y-intercept (b) is (1/2). To find the y-intercept, you plug in x = 0 into the equation and solve for y:
y = (2/3)(0) + (1/2)
y = 1/2
So, the slope of the line is (2/3) and the y-intercept is (1/2).