Consider the graph shown.
A graph is shown in the xy-plane. The values on the x-axis range from negative 8 to 8 in increments of 2 and the values on the y-axis range from negative 8 to 8 in increments of 2. A line is shown which passes through the points (0, 2), and (4, 4).
What is the slope of the graph?
Write an equation for the line.
please help i'm a little confused
as with any line, the slope is the change in y divided by the change in x. So, that would be
(2-4)/(0-4) = 1/2
Now, using the point-slope form of the line, with either point,
y-2 = 1/2 (x-0)
or
y-4 = 1/2 (x-4)
or in either case, this resolves to y = 1/2 x + 2
Use the slope formula, slope = (y2 - y1)/(x2 - x1)
Thank you! :3
Well, don't be confused! I'm here to help...and maybe make you smile too!
To find the slope of the graph, we can use the formula:
slope = (change in y) / (change in x)
So, let's calculate:
change in y = 4 - 2 = 2
change in x = 4 - 0 = 4
slope = 2 / 4 = 1/2
Now, let's move on to the equation for the line. We can use the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
Since we already know the slope is 1/2, all we need is to find the y-intercept. We can use the point (0, 2) for that. Plugging in the values:
2 = (1/2)(0) + b
2 = 0 + b
b = 2
So, the equation for the line is:
y = (1/2)x + 2
There you go! I hope that clears things up. If not, feel free to ask more questions, and I'll do my best to make you laugh while helping you out!
To find the slope of the graph, you can use the formula for slope:
slope = (change in y)/(change in x)
First, identify two points on the line. In this case, the given points are (0, 2) and (4, 4).
The change in y is the difference between the y-coordinates of the two points, which is 4 - 2 = 2.
The change in x is the difference between the x-coordinates of the two points, which is 4 - 0 = 4.
Now, substitute these values into the slope formula:
slope = 2/4 = 1/2
So, the slope of the graph is 1/2.
To write an equation for the line, you can use either the point-slope form or the slope-intercept form. Let's use the point-slope form:
y - y1 = m(x - x1)
Choose one of the given points, (0, 2), and plug in the values:
y - 2 = (1/2)(x - 0)
Simplify:
y - 2 = (1/2)x
Add 2 to both sides:
y = (1/2)x + 2
So, the equation of the line is y = (1/2)x + 2.