Sure, let's find the equation of the line passing through the points (-4,-2) and (3,3). The equation of a line in the slope-intercept form is y = mx + b where m is the slope and b is the y-intercept.
First, we calculate the slope (m) of the line. This can be done using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1,y1) and (x2,y2) are the coordinates of the two given points. Substituting the given points (-4,-2) as (x1,y1) and (3,3) as (x2,y2), the equation becomes:
m = (3 - (-2)) / (3 - (-4)) = 0.7142857142857143
So, the slope of the line m is approximately 0.714.
Next, we find the y-intercept (b) of the line. Using one of the points on the line (let's use (-4,-2) as (x1,y1)) and the slope, we can use the equation:
b = y1 - m*x1
Substituting the values, we get:
b = -2 - 0.714*(-4) = 0.8571428571428572
So, the y-intercept of the line b is approximately 0.857.
Hence, the equation of the line passing through (-4, -2) and (3, 3) is:
y = 0.714x + 0.857 which is approximately equal to y = 0.7142857142857143x + 0.8571428571428572.