Final answer:
To write the equation of the line that passes through the given points, we need to find the slope and y-intercept using the slope-intercept form. For the given points (2, -3) and (-7, -11), the equation is f(x) = -8/9x - 11/9.
Step-by-step explanation:
To write the equation of the line that passes through the given points using the slope-intercept form, we need to find the slope and the y-intercept. The slope, denoted by 'm', can be determined by using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points given. The y-intercept, denoted by 'b', can be found by substituting the coordinates of one point into the equation y = mx + b and solving for 'b'. Once we have the slope and the y-intercept, we can write the equation in the form y = mx + b, where y = f(x).
For the given points (2, -3) and (-7, -11), the slope is: m = (-11 - (-3)) / (-7 - 2) = -8/9. To find the y-intercept, we can choose either of the two points. Substituting (2, -3) into the equation y = mx + b, we get -3 = (-8/9)(2) + b. Solving for 'b', we have -3 = -16/9 + b, which implies that b = -3 + 16/9 = -27/9 + 16/9 = -11/9.
Therefore, the equation of the line that passes through the given points is: f(x) = -8/9x - 11/9, which is option A.
Learn more about Slope-intercept form