What is the equation of the line with a Y intercept of four and a point (8,8)?
A. Y=2x+8
B. Y=2x+4
C. Y=1/2x+8
D. Y=1/2x+4
I really don’t know I have searched and searched and I can’t find anything where it says I can use a y intercept and a point to make an equation. I don’t care about an answer I need and explination
y = m x + b
when x = 0, y = 4
4 = 0 + b
so b = 4
y = m x + 4
when x = 8, y = 8
8 = 8 m + 4
8 m = 4
m = 1/2
so
y = (1/2) x + 4
Thank you so much you were right
To find the equation of a line using the y-intercept and a point, you can use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
where (x1, y1) represents the given point and m represents the slope of the line.
Given that the y-intercept is 4, we know that the line intersects the y-axis at the point (0, 4). Therefore, the y-intercept is (0, 4).
The given point is (8, 8).
To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Substituting in the coordinates of the given point and the y-intercept, m = (8 - 4) / (8 - 0) = 4 / 8 = 1/2.
Now we have the slope (1/2) and a point (8, 8). We can substitute these values into the point-slope form:
y - 8 = 1/2(x - 8)
Simplifying the equation further:
y - 8 = 1/2x - 4
Adding 8 to both sides of the equation:
y = 1/2x + 4
Therefore, the equation of the line with a y-intercept of 4 and a point (8, 8) is y = 1/2x + 4, which corresponds to option D.
To find the equation of a line given a y-intercept and a point, you can use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope of the line and b represents the y-intercept.
In this case, you are given the y-intercept of 4, which means that the line intersects the y-axis at Y = 4. Therefore, the equation will have the form y = mx + 4.
Next, you are given a point on the line, (8,8). Now, you can use this point to find the slope (m) of the line. The slope of a line passing through two points, (x1, y1) and (x2, y2), is given by the formula m = (y2 - y1) / (x2 - x1).
Substituting the coordinates into the formula, you get:
m = (8 - 4) / (8 - 0)
m = 4 / 8
m = 1/2
Now that you have the slope (m = 1/2) and the y-intercept (b = 4), you can substitute these values into the slope-intercept form of a linear equation to find the equation of the line.
Therefore, the equation of the line with a y-intercept of 4 and a point (8,8) is y = 1/2x + 4.
Thus, the correct answer is D. Y = 1/2x + 4.