Final answer:
To write an equation in slope-intercept form of the line that passes through the points (-1,4) and (-2,1), we need to find the slope and the y-intercept. The slope can be found using the formula (y2 - y1) / (x2 - x1), and the y-intercept can be found by substituting the slope and one of the given points into the slope-intercept form equation. The equation of the line is y = 3x + 7.
Step-by-step explanation:
To write an equation in slope-intercept form of the line that passes through the points (-1,4) and (-2,1), we need to find the equation of the line.
The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the slope, we can use the formula: m = (y2 - y1) / (x2 - x1).
Substituting the coordinates (-1,4) and (-2,1) into the formula, we get: m = (1 - 4) / (-2 - (-1)) = -3 / -1 = 3.
Now that we have the slope, we can choose one of the given points to find the y-intercept. Let's use (-1,4).
Substituting the slope m = 3 and the coordinates (x, y) = (-1, 4) into the slope-intercept form equation, we get: 4 = 3(-1) + b.
Simplifying the equation, we have: 4 = -3 + b.
Now, solve for b:
Subtracting -3 from both sides, we have: 4 + 3 = b.
Therefore, the y-intercept b is 7.
Substituting the slope m = 3 and the y-intercept b = 7 into the slope-intercept form equation, we get the equation of the line: y = 3x + 7.