Final answer:
The equation in slope-intercept form of the line that passes through the given points (-4, 9) and (-2, 4) is y = -2x + 1.
Step-by-step explanation:
The equation in slope-intercept form of the line that passes through the given points (-4, 9) and (-2, 4) is y = -2x + 1.
To find the equation, we need to determine the slope (m) and the y-intercept (b). The slope can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. Substituting the given values, we have m = (4 - 9) / (-2 - (-4)) = -5 / 2 = -2.5.
Next, we can use the slope-intercept form, y = mx + b, to substitute the known values and solve for the y-intercept. Choosing one of the given points, (-4, 9), we have 9 = -2.5(-4) + b. Solving for b, we get b = 9 - 10 = -1.
Therefore, the equation in slope-intercept form that passes through the given points is y = -2x + 1.