Question

Find the equation for the function described below. (Let x be the independent variable and y be the dependent variable.) The linear function whose graph has passes through the points (−4, 3) and (3, −3)

Answer 1

First, let's find the slope of the line that passes through these two points. The formula for the slope (m) is:

m = (y2 - y1) / (x2 - x1)

Plugging in the coordinates of the two points gives us:

m = (-3 - 3) / (3 - (-4)) = -6 / 7 ≈ -0.857

Next, we can find the y-intercept (b) of the line. We can use the slope-intercept form equation for a line, which is:

y = mx + b

Rearranging the equation to solve for b and substituting point (-4, 3) and the slope that we figured out into the equation, we get:

b = y - mx = 3 - (-0.857 * -4) ≈ -3.428 ≈ -0.429

So, the equation of the line that passes through the points (-4, 3) and (3, -3) is:

y = -0.857x - 0.429