Final answer:
The equation of the line that passes through the points (0,1) and (−6,4) is y = −0.5x + 1, obtained by calculating the slope and applying the point-slope form.
Step-by-step explanation:
To find the equation of the line that passes through the points (0,1) and (−6,4), we first need to calculate the slope (m) of the line using the formula
m = (y2 − y1) / (x2 − x1).
Substituting the given points into the formula, we get
m = (4 − 1) / (−6 − 0) = 3 / −6 = −0.5.
Now that we have the slope, we can use the point-slope form of the equation, which is y − y1 = m(x − x1), where (x1, y1) is one of the given points.
Using the point (0,1), the equation becomes y − 1 = −0.5(x − 0), simplifying to y = −0.5x + 1.
This is the equation that represents the line passing through the two points.