Write the equation of the graph in the form of y=mx+b that matches
the illustration shows that line j's corrdnates are (0,8) and (3,0)and that k's are (-5,-5) and (0,-3) and L's coordnates are (0,-7) and (0,3)
Line j
Y=____x +____
Line K
y=____x+____
Line L
y=___x+____
Line j:
First, we need to find the slope (m) using the equation m = (y2 - y1) / (x2 - x1).
m = (0 - 8) / (3 - 0) = -8/3
Using the point-slope form of a line, y - y1 = m(x - x1):
y - 8 = (-8/3)(x - 0)
y - 8 = (-8/3)x
y = (-8/3)x + 8
So, the equation of line j is y = (-8/3)x + 8.
Line K:
First, we need to find the slope (m):
m = (-3 - (-5)) / (0 - (-5)) = 2/5
Using the point-slope form of a line, y - y1 = m(x - x1):
y - (-5) = (2/5)(x - (-5))
y + 5 = (2/5)(x + 5)
y = (2/5)x + 2 - 5
y = (2/5)x - 3
So, the equation of line K is y = (2/5)x - 3.
Line L:
Since the line passes through the points (0, -7) and (0, 3), the x-coordinate is constant, which means the line is vertical and the equation will be in the form x = a, where a is the x-coordinate.
So, the equation of line L is x = 0.
so whats the last one
Apologies for the confusion. Let's solve for the equation of Line L again.
Line L:
Since Line L is vertical and passes through the points (0, -7) and (0, 3), the x-coordinate remains constant for all y-values. Therefore, the equation of Line L is simply x = 0.
So, the equation of Line L is x = 0.
what remember y=mx+b
Apologies for the confusion. Let's solve for the equation of Line L again using the slope-intercept form.
Line L:
Since the line passes through the points (0, -7) and (0, 3), the x-coordinate is constant, which means the line is vertical and the equation will be in the form x = a. In this case, the y-intercept (b) is -7, and the equation will be y = mx + b.
Since the slope (m) is undefined for a vertical line, the equation of Line L is x = 0.
try a different solution
Apologies for the mistake. Let's solve for the equation of Line L again using the slope-intercept form.
Line L:
To find the equation of Line L, we need to find the slope (m) first. The slope is calculated as m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
In this case, the line passes through the points (0, -7) and (0, 3).
m = (3 - (-7)) / (0 - 0) = 10 / 0
The slope (m) is undefined since the denominator is zero. Therefore, the equation of Line L cannot be expressed in the form y = mx + b.
Instead, for Line L, the equation is x = 0, indicating a vertical line passing through the x-intercept at x = 0.