Answer and Step-by-step explanation:
To find the slope-intercept form of the line through (-5, 3) that is perpendicular to the vertical line passing through (0, -1), we need to determine the slope of the given vertical line and then find the negative reciprocal of that slope.
The vertical line passing through (0, -1) is a vertical line with an undefined slope. This is because vertical lines have no change in x-coordinate (Δx) and any change in y-coordinate (Δy) results in an undefined slope (Δy/Δx).
Since the slope of the vertical line is undefined, we can say that its equation is x = 0.
Now, since the line we are looking for is perpendicular to this vertical line, the slope of our line will be the negative reciprocal of the undefined slope. The negative reciprocal of an undefined slope is 0.
Now we have the slope (m) as 0 and a point (-5, 3) on the line. We can use the point-slope form of a line to find the equation.
The point-slope form of a line is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.
Substituting the values, we have:
y - 3 = 0(x - (-5))
y - 3 = 0(x + 5)
y - 3 = 0
y = 3
Therefore, the slope-intercept form of the line through (-5, 3) that is perpendicular to the vertical line passing through (0, -1) is y = 3.