Firstly, let's recall that the slope-intercept form of the linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the slope (m), we'll need two points on the line. Here, we already have two points (-5,3) and (-3,11). Now, we'll use the formula:
m = (y2 - y1) / (x2 - x1)
We are given x1 = -5, y1 = 3 and x2 = -3, y2 = 11.
So substituting these values into our formula,we get the slope as:
m = (11 - 3) / (-3 - -5) = 8/2 = 4
Now, our half task is done. We found the slope, m = 4.
Next we'll calculate the y-intercept (b).
We'll use the formula for a line which is y = mx + b
Since we know the slope 'm' and we have a point on the line, we can use this to find the y-intercept 'b'.
So either using point (-5,3) or (-3,11) doesn't matter, you'll get the same answer. Let's use the point (-5,3), substituting these:
3 = 4(-5) + b
3 = -20 + b
Adding 20 to both sides, we get
b = 23
We have our y-intercept now, which is b = 23.
So, the equation of line in slope intercept form is: y = 4x + 23.