Final answer:
The equation of the straight line that goes through points P(-2, -8) and Q(3, 2) is y = 2x - 4.
Step-by-step explanation:
The equation of a straight line that goes through points P(-2, -8) and Q(3, 2) can be found using the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
- First, find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1).
Plugging in the coordinates (x1, y1) = (-2, -8) and (x2, y2) = (3, 2), we get m = (2 - (-8)) / (3 - (-2)) = 10 / 5 = 2. - Next, use one of the given points and the slope to find the y-intercept (b) by substituting the values into the equation: y = mx + b.
Using the point (-2, -8) and the slope m = 2, we can solve for b: -8 = 2(-2) + b.
Simplifying, we get -8 = -4 + b. By adding 4 to both sides, we find b = -4. - Finally, write the equation of the line using the values of m and b.
Substituting m = 2 and b = -4 into the equation y = mx + b, we have y = 2x - 4.
Therefore, the equation of the straight line that goes through points P(-2, -8) and Q(3, 2) is y = 2x - 4.