Answer:
The equation of the line that passes through the points (-7, -3) and (5, 6) is y = (3/4)x + 9/4.
Explanation:
To find the equation of a line that passes through the points (-7, -3) and (5, 6), we can use the slope-intercept form of a linear equation, which is y = mx + b. In this form, m represents the slope of the line, and b represents the y-intercept.
Step 1: Find the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates (-7, -3) and (5, 6) into the formula, we get:
m = (6 - (-3)) / (5 - (-7))
m = 9 / 12
m = 3/4
Step 2: Use one of the points and the slope to find the value of b in the equation y = mx + b. Let's use the point (-7, -3):
-3 = (3/4)(-7) + b
-3 = -21/4 + b
To find b, we can add 21/4 to both sides of the equation:
-3 + 21/4 = b
-12/4 + 21/4 = b
9/4 = b
Step 3: Write the equation of the line using the slope (m) and the y-intercept (b):
y = (3/4)x + 9/4
Therefore, the equation of the line that passes through the points (-7, -3) and (5, 6) is y = (3/4)x + 9/4.