Final answer:
To find the equation in slope-intercept form, we first calculate the slope using the formula and then use the slope-intercept form equation y = mx + b to find the y-intercept and write the equation.
Step-by-step explanation:
To find the equation in slope-intercept form of the line that passes through the points (7,-4) and (14,-12), we need to find the slope of the line first. The slope (m) can be found using the formula: m = (y2 - y1) / (x2 - x1). Plugging in the values, we get m = (-12 - (-4)) / (14 - 7) = -8 / 7.
Next, we can use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. We can substitute the slope and one of the given points to find the value of b. Using the point (7,-4), we have -4 = (-8 / 7) * 7 + b. Solving for b, we get b = -4 - (-8) = 4.
Finally, we can write the equation in slope-intercept form as y = (-8 / 7)x + 4.
Learn more about equation in slope-intercept form