Final answer:
To write a linear equation in slope-intercept form using two given points, we need to find the slope and the y-intercept. The slope can be found using the formula m = (y2 - y1) / (x2 - x1), and the y-intercept can be found by substituting the slope and a point into the equation. The equation for the given points (-6, -7) and (3, -4) is y = (1/3)x - 5.
Step-by-step explanation:
To write a linear equation in slope-intercept form, we need to find the slope and the y-intercept. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by m = (y2 - y1) / (x2 - x1). Using the points (-6, -7) and (3, -4), we can find the slope:
m = (-4 - (-7)) / (3 - (-6)) = 3/9 = 1/3
Now, we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept. We can substitute the slope and one of the points to find b:
-7 = (1/3)(-6) + b
-7 = -2 + b
b = -5
Therefore, the linear equation in slope-intercept form is y = (1/3)x - 5.