Final answer:
To find the equation of a line using two given points (4,4) and (1,1), we first calculate the slope using the formula m = (y2 - y1) / (x2 - x1). Then, we use the point-slope form y - y1 = m(x - x1) to find the equation. The equation is simplified to the slope-intercept form y = -3x + 16.
Step-by-step explanation:
To find the equation of a line using the points (4,4) and (1,1), we first need to find the slope of the line. The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1,y1) and (x2,y2) are the coordinates of the two points. Plugging in the values, we get m = (1 - 4) / (1 - 4) = -3.
Now that we have the slope, we can use the point-slope form of a linear equation which is y - y1 = m(x - x1), where (x1,y1) is one of the given points and m is the slope. Using the point (4,4) and the slope -3, the equation becomes:
y - 4 = -3(x - 4)
Simplifying the equation, we get y - 4 = -3x + 12. Rearranging the terms, the equation can be written as y = -3x + 16. This is the slope-intercept form of the linear equation.