Write an equation in slope intercept form when given two pieces of key information about the line
Goes through the points (0,4) and (2,7)
To find the equation of the line in slope-intercept form, we need to determine the slope of the line and the y-intercept.
The slope of a line can be calculated using the formula:
slope (m) = (change in y) / (change in x) = (y2 - y1) / (x2 - x1).
From the given points (0,4) and (2,7), we can calculate the slope:
slope = (7 - 4) / (2 - 0) = 3 / 2 = 1.5.
Now that we have the slope, we can use the slope-intercept form of a line, which is y = mx + b, where m represents the slope and b represents the y-intercept.
We can substitute the slope (m = 1.5) and one of the given points (0,4) into the equation to solve for the y-intercept (b):
y = mx + b
4 = 1.5(0) + b
4 = 0 + b
b = 4.
Therefore, the equation of the line in slope-intercept form is:
y = 1.5x + 4.